Recent questions in Application of Derivatives

The function $ \Large\frac{\sin(x+\alpha)}{\sin(x+\beta)}$ has no maximum or minimum value if \[(a)\;\beta-\alpha=k\pi\qquad(b)\;\beta-\alpha \neq k\pi\qquad(c)\;\beta-\alpha = 2k\pi\qquad(d)\;None\; of\; these\; where\; k\; is\; an\; integer.\]

asked Jan 28, 2013 by meena.p

0 answers

If $f(x)= \left\{ \begin{array}{1 1} 3x^2+12x-1 & \quad :\;-1\leq x \leq 2 \\37-x & \quad :\;2<x\leq 3 \end{array} \right. $ then\[\begin{array}{1 1}(a)\;f(x)\; is\; increasing\; on\; [-1,2]\\(b)\;f(x)\; is\; continuous\; on\; [-1,3]\\(c)\;f'(2) doesn't \;exist\\(d)\;f(x)\; has\; the\; maximum\; value\; at x = 2\end{array}\]

asked Jan 28, 2013 by meena.p

0 answers

If $\theta$ is the semivertical angle of a cone of maximum volume and given slant height, then $\tan \theta$ is given by \[(a)\;2\qquad(b)\;1\qquad(c)\;\sqrt 2\qquad(d)\;\sqrt 3\]

asked Jan 28, 2013 by meena.p

0 answers

If $ y=a log|x|+bx^2+x $ has its extreme values at x = 1 and x = 2 then\[(a)\;a=2,b=-1\qquad(b)\;a=2,b=-1/2\qquad(c)\;-2,b=1/2\qquad(d)\;none\;of\;these\]

asked Jan 28, 2013 by meena.p

0 answers

The difference between the greatest and the least values of the function $ f(x)=\large\cos x+\large\frac{1}{2}\cos 2x-\frac{1}{3}\cos 3x $ is \[(a)\;2/3\qquad(b)\;8/7\qquad(c)\;9/4\qquad(d)\;3/8\]

asked Jan 28, 2013 by meena.p

0 answers

The co-ordinates of the point p(x,y) in the first quadrant on the ellipse $\Large\frac{ x^2}{8}+\frac{y^2}{18}$=1 so that the area of the triangle formed by the tangent at P and the co-ordinate axes is the smallest are given by \[(a)\;(2,3)\qquad(b)\;(\sqrt 8,0)\qquad(c)\;(\sqrt {18}, 0)\qquad(d)none\;of\;these\]

asked Jan 28, 2013 by meena.p

0 answers

The value of a for which the function $ f(x)=a\sin(x)+\frac{1}{3}\sin 3x.$has an extreme at $ x=\frac{\pi}{3}$ is\[(a)\;1\qquad(b)\;-1\qquad(c)\;0 \qquad(d)\;2\]

asked Jan 28, 2013 by meena.p

0 answers

The function $y=\tan^{-1}x-x $ decreases in the interval of \[(a)\;(1,\infty)\qquad(b)\;(-1,\infty)\qquad(c)\;(-\infty,\infty)\qquad(d)\;(0,\infty)\]

asked Jan 28, 2013 by meena.p

0 answers

The function $ f(x)=2 log (x-2) - x^2+4x+1 $increases in the interval.\[(a)\;(1,2)\qquad(b)\;(2,3)\qquad(c)\;(5/2,3)\qquad(d)\;(2,4)\]

asked Jan 28, 2013 by meena.p

1 answer

The slope of the tangent to the curve represented by $ x=t^2+3t-8\;and\;y=2t^2-2t-5$at the point M(2,-1) is \[(a)\;\frac{7}{6}\qquad(b)\;\frac{2}{3}\qquad(c)\;\frac{3}{2}\qquad(d)\;\frac{6}{7}\]

asked Jan 28, 2013 by meena.p

0 answers

The least value of the function $f(x)=ax+\frac{b}{x}(a>0,b>0,x>0)$ is ___________.

asked Jan 12, 2013 by sreemathi.v

1 answer

The function $f(x)=\Large\frac{2x^2-1}{x^4}$,x>0,decreases in the interval__________.

asked Jan 12, 2013 by sreemathi.v

1 answer

The value of a for which the function $f(x)=sin x-ax+b$ increases on R are__________.

asked Jan 12, 2013 by sreemathi.v

1 answer

The equation of normal to the curve y=tan x at (0,0) is___________.

asked Jan 12, 2013 by sreemathi.v

1 answer

The curves $y=4x^2+2x-8$ and $y=x^3-x+13$ touch each other at the point_________.

asked Jan 12, 2013 by sreemathi.v

1 answer

The maximum value of $\Large\frac{1}{x}$ is:

asked Jan 12, 2013 by sreemathi.v

1 answer

$f(x)=x^x$ has a stationary point at

asked Jan 12, 2013 by sreemathi.v

1 answer

Maximum slope of the curve $y=x^3+3x^2+9x-27$ is

asked Jan 12, 2013 by sreemathi.v

1 answer

At $x=\Large\frac{5}{6}$$,f(x)=2\sin 3x+3\cos 3x$ is:

asked Jan 12, 2013 by sreemathi.v

1 answer

The maximum value of sin x,cos x is

asked Jan 12, 2013 by sreemathi.v

1 answer