Chapter 10: Problem 881
The rate of change of function \(\mathrm{f}(\mathrm{x})=3 \mathrm{x}^{5}-5 \mathrm{x}^{3}+5 \mathrm{x}-7\) is minimum when \(\mathrm{x}\) is (a) 0 (b) \((1 / \sqrt{2})\) (c) \(\sqrt{2}\) (d) \(\pm(1 / \sqrt{2})\)
Chapter 10: Problem 881
The rate of change of function \(\mathrm{f}(\mathrm{x})=3 \mathrm{x}^{5}-5 \mathrm{x}^{3}+5 \mathrm{x}-7\) is minimum when \(\mathrm{x}\) is (a) 0 (b) \((1 / \sqrt{2})\) (c) \(\sqrt{2}\) (d) \(\pm(1 / \sqrt{2})\)
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Get started for freeIf \(x^{2} e^{y}+2 x y e^{x}+23=0\) then \((d y / d x)=\) (a) \(2 \mathrm{xe}^{\mathrm{y}-\mathrm{x}}+2 \mathrm{y}(\mathrm{x}+1)\) (b) \(2 \mathrm{xe}^{\mathrm{x}-\mathrm{y}}-3 \mathrm{y}(\mathrm{x}+1)\) (c) \(\left[\left\\{-2 x e^{y}-e^{x} \cdot 2 y(x+1)\right\\} /\left\\{x\left(x e^{y}+e^{x} \cdot 2\right)\right\\}\right]\) (d) \(2 \mathrm{xe}^{\mathrm{y}-\mathrm{x}}-\mathrm{y}(\mathrm{x}+1)\)
The second order derivative of a \(\sin ^{3} \propto\) with respect to a \(\cos ^{3} \propto\) at \(\alpha=(\pi / 4)\) (a) \([(4 \sqrt{2}) / 3 \mathrm{a}]\) (b) 2 (c) \([1 /(12 \mathrm{a})]\) (d) 0
If \(y=(x \log x)^{\log \log x}\) for \((d y / d x)=A^{\log \log x-1}(B+(\log x+2) \log\) \(\log x\) ) then \(A B=\) (a) \(x \log x\) (b) \(x(\log x)^{2}\) (c) \(x^{2} \cdot \log x\) (d) \(\log x\)
If \(\mathrm{y}=\tan ^{-1}\left[1 /\left(\mathrm{x}^{2}+\mathrm{x}+1\right)\right] \tan ^{-1}\left[1 /\left(\mathrm{x}^{2}+3 \mathrm{x}+3\right)\right]\) \(+\tan ^{-1}\left[1 /\left(\mathrm{x}^{2}+5 \mathrm{x}+7\right)\right] \ldots \ldots\) to \(\mathrm{n}\) terms then \((\mathrm{dy} / \mathrm{d} \mathrm{x})\) \(=\) (a) \(\left[1 /\left\\{1+(\mathrm{x}+\mathrm{n})^{2}\right\\}\right]+\left[1 /\left(1+\mathrm{x}^{2}\right)\right]\) (b) \(\left[1 /\left\\{1+(\mathrm{x}+\mathrm{n})^{2}\right\\}\right]-\left[1 /\left(1+\mathrm{x}^{2}\right)\right]\) (c) \(\left[2 /\left\\{1+(\mathrm{x}+\mathrm{n})^{2}\right\\}\right]+\left[1 /\left(1+\mathrm{x}^{2}\right)\right]\) (d) \(\sum \mathrm{n}\)
The function \(\mathrm{f}(\mathrm{x})=2 \log (\mathrm{x}-2)-\mathrm{x}^{2}+4 \mathrm{x}+1\) increasing on the interval (a) \((2,3)\) (b) \((1,2)\) (c) \((2,4)\) (d) \((1,3)\)
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