91Ó°ÊÓ

In Exercises 17 through 20, sketch the graph of a function \(f\) that has all the given properties. a. \(f^{\prime}(x)>0\) when \(x<0\) and when \(x>5\) b. \(f^{\prime}(x)<0\) when \(00\) when \(-62\) d. \(f^{\prime \prime}(x)<0\) when \(x<-6\) and when \(-3

In Exercises 17 through 20, sketch the graph of a function \(f\) that has all the given properties. a. \(f^{\prime}(x)>0\) when \(x<-2\) and when \(-23\) c. \(f^{\prime}(-2)=0\) and \(f^{\prime}(3)=0\)

In Exercises 17 through 20, sketch the graph of a function \(f\) that has all the given properties. a. \(f^{\prime}(x)>0\) when \(12\) c. \(f^{\prime \prime}(x)>0\) for \(x<2\) and for \(x>2\) d. \(f^{\prime}(1)=0\) and \(f^{\prime}(2)\) is undefined.

In Exercises 17 through 20, sketch the graph of a function \(f\) that has all the given properties. a. \(f^{\prime}(x)>0\) when \(x<1\) b. \(f^{\prime}(x)<0\) when \(x>1\) c. \(f^{\prime \prime}(x)>0\) when \(x<1\) and when \(x>1\) d. \(f^{\prime}(1)\) is undefined.

In Exercises 21 through 24 , find all critical numbers for the given function \(f(x)\) and use the second derivative test to determine which (if any) critical points are relative maxima or relative minima. $$ f(x)=-2 x^{3}+3 x^{2}+12 x-5 $$

In Exercises 21 through 24 , find all critical numbers for the given function \(f(x)\) and use the second derivative test to determine which (if any) critical points are relative maxima or relative minima. $$ f(x)=x(2 x-3)^{2} $$

In Exercises 21 through 24 , find all critical numbers for the given function \(f(x)\) and use the second derivative test to determine which (if any) critical points are relative maxima or relative minima. $$ f(x)=\frac{x^{2}}{x+1} $$

In Exercises 21 through 24 , find all critical numbers for the given function \(f(x)\) and use the second derivative test to determine which (if any) critical points are relative maxima or relative minima. $$ f(x)=\frac{1}{x}-\frac{1}{x+3} $$

In Exercises 25 through 28, find the absolute maximum and the absolute minimum values (if any) of the given function on the specified interval. $$ f(x)=-2 x^{3}+3 x^{2}+12 x-5 ;-3 \leq x \leq 3 $$

In Exercises 25 through 28, find the absolute maximum and the absolute minimum values (if any) of the given function on the specified interval. $$ f(t)=-3 t^{4}+8 t^{3}-10 ; 0 \leq t \leq 3 $$