The function \( f(x) \) defined for all real numbers \( \mathrm{x} \) has the following properti...

Channel:
PW Solutions
Subscribers:
447,000
Published on ● Video Link: https://www.youtube.com/watch?v=S_bPlXsgj6k


Duration: 9:11
3 views
0

The function \( f(x) \) defined for all real numbers \( \mathrm{x} \) has the following properties
\( f^{\prime}(x)=k\left(2 x-x^{2}\right) e^{-x} \) for some constant \( k0 \). Find
(a) The intervals on which \( f \) is increasing and decreasing and any local maximum or minimum values.
(b) The intervals on which the graph \( f \) is concave down and concave up.
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live



Other Videos By PW Solutions


2023-06-08Let \( f(x)=\left\{\begin{array}{cc}x^{3}-x^{2}+10 x-7, & x \leq 1 \\ -2 x+\log _{2}\left(b^{2}-...
2023-06-08If the absolute maximum value of the function \[ f(x)=\left(x^{2}-2 x+7\right) e^{\left(4 x^{3}-...
2023-06-08Consider the function \( y=f(x)=\ln (1+\sin x) \) with \( -2 \pix \) \( 2 \pi \). Find (a) The z...
2023-06-08Sketch a possible graph of a differentiable function \( f \) that satisfies the following condit...
2023-06-08Consider the function \( f(x)=\left[\begin{array}{cc}\sqrt{x} \ln x & \text { when } x0 \\ 0 & \...
2023-06-08For \( f(x)=\frac{-x^{2}+4 x-7}{x-1} \) (a) Determine the equations of its asymptotes. (b) Find ...
2023-06-08The position of a particle moving along the \( \mathrm{x} \)-axis is given by \( x(t)=t^{3}-9 t^...
2023-06-08Let \( f(x) \) be a differentiable and \( \mathrm{g}(\mathrm{x}) \) be a twice differentiable fu...
2023-06-08Each of the following represents a graph of a functions derivative. Sketch a possible graph for ...
2023-06-08Let \( f(x) \) be a real valued function such that \( f(x)=\frac{2 x-1}{x-2} \forall x \in \) \(...
2023-06-08The function \( f(x) \) defined for all real numbers \( \mathrm{x} \) has the following properti...
2023-06-08Prove that for the curves \( a x^{2}+2 h x y+b y^{2}+2 g x+2 f y+c= \) 0 , at point \( p\left(x_...
2023-06-08Obtain the maximum and minimum values of the expression \( \frac{x^{2}-2 x \cos \alpha+1}{x^{2}-...
2023-06-08If \( f:[0, \pi / 2] \rightarrow[0,1] \) be a differentiable function such that \( f(0)=0 \) and...
2023-06-08Let \( P(x) \) be a polynomial with real coefficients. Let \( a, b \in R \), \( ab \) be the two...
2023-06-08Let \( f(x) \) be a non-constant thrice differential function defined on \( (-\infty, \infty) \)...
2023-06-08An idealized hourglass is made by joining two identical circular cones, each with base radius \(...
2023-06-08Prove that \( \sin xx-\frac{x^{3}}{6}+\frac{x^{5}}{120} \) for \( x0 \)
2023-06-08Let \( f(x)=1-x-4 x^{3} \); find all real values of \( x \) satisfying the inequality \( 1-f(x)-...
2023-06-08If \( f(x)=2 x^{3}-3 x^{2}+1 \) then number of distinct real solutions of the equation \( f(f(x)...
2023-06-08The complete set of non-zero values of \( k \) such that the equation \( \left|x^{2}-7 x+6\rig...