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Recent questions tagged p206

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

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