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Recent questions tagged ch6

Find the equation of the normals to the curve $y = x^3 + 2x + 6$ which are parallel to the line $x + 14y + 4 = 0$.

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find the equation of the normal at the point \((am^2,am^3)\) for the curve \(ay^2 = x^3.\)

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find the points on the curve \(x^2 + y^2 - 2x - 3 = 0\) at which the tangents are parallel to the \(x\) - axis.

asked Nov 24, 2012 by thanvigandhi_1

1 answer

For the curve $y = 4x^3 – 2x^5$, find all the points at which the tangent passes through the origin.

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find the points on the curve $y = x^3$ at which the slope of the tangent is equal to the $y$ - coordinate of the point.

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Show that the tangents to the curve \(y = 7x^3 + 11\) at the points where \(x = 2\) and \(x = -2\) are parallel.

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find the equation of the tangent line to the curve $y = x^2 - 2x +7$ which is $(a)$ parallel to the line $2x - y + 9 = 0$

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find the equations of the tangent and normal to the given curves at the indicated points: $ y = x^4 - 6x^3 + 13x^2 - 10x + 5\; at \;(0, 5)$

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find points on the curve $ \large\frac{x^2}{9} + \frac{y^2}{16} = 1$ at which the tangents are $(i)\; parallel\; to\; x - axis$

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find the equation of all lines having slope $0$ that are tangents to the curve $ y=\large \frac{1}{x^2-2x+3}$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the equation of all lines having slope \(2\) that are tangents to the curve $ y= \large\frac{1}{x-3}, $$\: x \neq 3$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the equation of all lines having slope $–1$ that are tangents to the curve $ y= \large\frac{1}{x-1}, $$ \: x \neq 1$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the point on the curve $y = x^3 - 11x + 5$ at which the tangent is $y = x -11$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find a point on the curve $y = (x – 2)^2 $ at which the tangent is parallel to the chord joining the points $(2, 0)$ and $(4, 4)$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find points at which the tangent to the curve $y = x^3 - 3x^2 - 9x + 7$ is parallel to the $x$ - axis.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the slope of the normal to the curve $ x = 1 - a \sin\theta, y = b \cos^2\theta$ at $ \theta = \Large {\frac{\pi}{2}}$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the slope of the normal to the curve $ x = a \cos^3\theta, \: y = a \sin^3\theta$ at $ \theta =\Large {\frac{\pi}{4}}$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the slope of the tangent to the curve $y = x^3 - 3x + 2$ at the point whose $x$ - coordinate is $3$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the slope of the tangent to curve $ y = x^3 - x + 1$ at the point whose $x$ - coordinate is $2$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the slope of the tangent to the curve $\normalsize y =\large { \frac{x-1}{x-2},} \normalsize x \neq 2\; at\;x = 10$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the slope of the tangent to the curve $y = 3x^4 – 4x \; at\; x = 4.$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

The interval in which $y = x^2 e ^{- x}$ is increasing is

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Prove that the function given by \(f (x) = x^3 – 3x^2 + 3x - 100\) is increasing in \(R.\)

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Prove that the function \(f\) given by $f (x) = \log \cos\: x$ is strictly decreasing on $ \left(0, \: \large {\frac{\pi}{2}}\right)$ and strictly increasing on, $\left( \large {\frac{\pi}{2},} \normalsize \pi\right)$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Prove that the function $f$ given by $f (x) = \log \sin x$ is strictly increasing on$ \left(0, \: \large {\frac{\pi}{2}}\right)$ and strictly decreasing on $\left( \large {\frac{\pi}{2}}, \pi\right)$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Let $I$ be any interval disjoint from $[–1, 1]$. Prove that the function $f$ given by \( f(x) = x + \frac{1}{\large x}\) is strictly increasing on $I$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the least value of a such that the function $f$ given by $f (x) = x^2 + ax + 1$ is strictly increasing on $(1, 2).$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

On which of the following intervals is the function $f $ given by $f (x) = x^{100} + sin x –1$ strictly decreasing ?

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Which of the following functions are strictly decreasing on $\left(0, \: \large {\frac{\pi}{2}}\right)$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Prove that the function \(f\) given by \(f (x) = x^2 – x + 1\) is neither strictly increasing nor strictly decreasing on \((– 1, 1).\)

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Prove that the logarithmic function is strictly increasing on $(0, \infty).$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Prove that \( y =\large { \frac{4\sin\theta}{(2+\cos\theta)}}-\normalsize \theta\) is an increasing function of \(\theta\) in $\left[0, \: \large {\frac{\pi}{2}}\right]$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the values of $x$ for which $y = [x(x – 2)]^2$ is an increasing function.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Show that $ y = log(1+x)-\large {\frac{2x}{2+x}}, \normalsize x > – \normalsize 1$, is an increasing function of $x$ throughout its domain.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the intervals in which the following functions are strictly increasing or decreasing: $(a) \;x^2 + 2x - 5$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the intervals in which the function f given by $f (x) = 2x^3 – 3x^2 – 36 x + 7$ is (a) strictly increasing and (b) strictly decreasing ?

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the intervals in which the function $f$ given by $f (x) = 2x^2 - 3x$ is $(a) $ strictly increasing

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Show that the function given by $f (x) = \sin x$ is neither increasing nor decreasing in $(0, \pi)$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Show that the function given by $f (x) = \sin x$ is strictly decreasing in $(\large {\frac{\pi}{2}},$$ \pi)$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Show that the function given by \(f (x) = \sin \;x\) is strictly increasing in $\left(0, \: \large {\frac{\pi}{2}}\right)$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Show that the function given by $f(x) = e^{2x}$ is strictly increasing on $R$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Show that the function given by \(f (x) = 3x + 17\) is strictly increasing on \(R\).

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the total revenue in Rupees received from the sale of $x$ units of a product is given by $Rx = 3x^2 +36x + 5$. The marginal revenue, when $x = 15$ is

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the rate of change of the area of a circle with respect to its radius $r$ at $r = 6$ cm is

asked Nov 23, 2012 by thanvigandhi_1

1 answer

The total revenue in Rupees received from the sale of $x$ units of a product is given by $ R(x) = 13x^2 + 26x + 15.$ Find the marginal revenue when $x = 7$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

The total cost $C(x)$ in Rupees associated with the production of $x$ units of an item is given by $ C(x) = 0.007x^3 - 0.003x^2 + 15x + 4000.$ Find the marginal cost when 17 units are produced.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Sand is pouring from a pipe at the rate of $12 cm^3/s$. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?

asked Nov 23, 2012 by thanvigandhi_1

1 answer

A balloon, which always remains spherical, has a variable diameter $\large\frac{3}{2}$$(2x+1)$. Find the rate of change of its volume with respect to $x.$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

The radius of an air bubble is increasing at the rate of $ \large\frac{1}{2}$ cm/s. At what rate is the volume of the bubble increasing when the radius is $1\; cm$?

asked Nov 23, 2012 by thanvigandhi_1

1 answer

A particle moves along the curve $ 6y = x^3 +2$. Find the points on the curve at which the $y$-coordinate is changing $8$ times as fast as the $x$-coordinate.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

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