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Home Question Bank Math Calculus Archive 2024 November 02

Calculus Questions from Nov 02,2024

Browse the Calculus Q&A Archive for Nov 02,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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2. Encontrar los intervalos de crecimiento y decrecimiento de la función \( f(x)=\frac{x^{2}}{x-1} \) \( y ^ { \prime \prime } - 2 y ^ { \prime } + y = e ^ { x } + y = C _ { 1 } e ^ { x } + C _ { 2 } x e ^ { x } + \frac { x ^ { 2 } e ^ { x } } { 2 } \) Consider the function \( f(x)=-2 x^{2}+8 x-5 \). Determine, without graphing. whether the function has a minimum value or a maximum value. b. Find the minimum or maximum value and determine where it occurs. c. Identify the function's domain and its range. a. The function has a value. Consider the function \( f(x)=2 x^{2}-20 x-6 \). a. Determine, without graphing, whether the function has a minimum value or a maximum value. b. Find the minimum or maximum value and determine where it occurs. c. Identify the function's domain and its range. a. The function has a 28.The slope of the tangent at any point \( (x, y) \) on the curve \( y=f(x) \) is equal to \( 3 x^{2}-6 x-9 \) and the local maximum value of the function \( f \) is 17 , then the local minimum value of the function \( f \) equal \( \begin{array}{llll}\text { (a) }-17 & \text { (b) }-15 & \text { (c) } 7 & \text { (d) } 15\end{array} \) Ig. If the slope of the normal to the curve \( y=f(X) \) at any point on it is \( (2 y+1) \csc x \) if we know that the curve passes through the origin point, then its equation is \( \begin{array}{ll}\text { (a) } y^{2}+y=\sin x-1 & \text { (b) } y^{2}+y=\cos x-1 \\ \text { c) } y^{2}+y \csc y \cot y=0 & \text { (d) } y^{2}+y=(\sin x)^{-2}\end{array} \) 15. If slope of the tangent to the curve \( y=f(x) \) at any point on it equals \( \sec ^{2} x-\sin x \), the curve passes through the point \( \left(\frac{\pi}{4}, \frac{1}{\sqrt{2}}\right) \), then the equation is … \( \begin{array}{ll}\text { (a) } y=\frac{1}{3} \sec ^{3} x+\cos x-1 & \text { (b) } y=\tan x-\cos x-1 \\ \text { c } y=\tan x+\cos x-1\end{array} \) 12.If \( \hat{f}^{\prime}(X)=\frac{1}{2}\left[\mathrm{e}^{x}+\mathrm{e}^{-x}\right], f(0)=1, \grave{f}(0)=0 \), then \( f(x) \) equals \( \cdots \) \( \begin{array}{llll}\text { (a) }-f^{\prime}(x) & \text { (b) } f^{\prime}(x) & \text { (c) }-\stackrel{\rightharpoonup}{f}(x) & \text { (d) } \hat{f}^{\prime}(x)\end{array} \) \( R = - \frac { 4 } { 9 } x ^ { 3 } + 4 x ^ { 2 } + 6 , \quad 0 \leq x \leq 7 \) Find the point of diminishing returns for the function \( R=-\frac{4}{9} x^{3}+4 x^{2}+6, \quad 0 \leq x \leq 7 \)
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