91Ó°ÊÓ

Identify the critical points and find the maximum value and minimum value on the given interval. $$ f(x)=x^{4}-2 x^{2}+2 ; I=[-2,2] $$

A function is defined and a closed in terval is given. Decide whether the Mean Value Theorem applies to the given function on the given interval. If it does, find all possible values of \(c ;\) if not, state the reason. In each problem, sketch the graph of the given function on the given interval. $$ g(x)=x^{5 / 3} ;[0,1] $$

In Problems \(11-18,\) use the Concavity Theorem to determine where the given function is concave up and where it is concave down. Also find all inflection points. $$ T(t)=3 t^{3}-18 t $$

Find the critical points and use the test of your choice to decide which critical points give a local maximum value and which give a local minimum value. What are these local maximum and minimum values? $$ H(x)=x^{4}-2 x^{3} $$

Find the general antiderivative \(F(x)+C\) for each of the following. $$ f(x)=27 x^{7}+3 x^{5}-45 x^{3}+\sqrt{2} x $$

In Problems \(13-19,\) a function \(f\) is given with domain \((-\infty, \infty) .\) Indicate where \(f\) is increasing and where it is concave down. \(f(x)=3 x-x^{2}\)

Use Newton's Method to approximate the indicated root of the given equation accurate to five decimal places. Begin by sketching a graph. The positive root of \(2 x^{2}-\sin x=0\)

Identify the critical points and find the maximum value and minimum value on the given interval. $$ f(x)=x^{5}-\frac{25}{3} x^{3}+20 x-1 ; I=[-3,2] $$

A function \(f\) is given with domain \((-\infty, \infty) .\) Indicate where \(f\) is increasing and where it is concave down. \(f(x)=x^{9}\)

A function is defined and a closed in terval is given. Decide whether the Mean Value Theorem applies to the given function on the given interval. If it does, find all possible values of \(c ;\) if not, state the reason. In each problem, sketch the graph of the given function on the given interval. $$ g(x)=x^{5 / 3} ;[-1,1] $$