91Ó°ÊÓ

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. $$ q(x)=x^{4}-6 x^{3}-24 x^{2}+3 x+1 $$

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? $$ r(s)=3 s+s^{2 / 5} $$

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. $$ f(x)=x^{4}+8 x^{3}-2 $$

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

Find the \(x y\) -equation of the curve through (1,2) whose slope at any point is three times the square of its \(y\) -coordinate.

Identify the critical points and find the maximum value and minimum value on the given interval. $$ f(x)=\frac{x}{1+x^{2}} ; I=[-1,4] $$

A function \(f\) is given with domain \((-\infty, \infty) .\) Indicate where \(f\) is increasing and where it is concave down. \(f(x)=-2 x^{3}-3 x^{2}+12 x+1\)

Use Newton's Method to calculate \(\sqrt[4]{47}\) to five decimal places.

In Problems \(17-20,\) approximate the values of \(x\) that give maximum and minimum values of the function on the indicated intervals. $$ f(x)=x^{4}+x^{3}+x^{2}+x ;[-1,1] $$

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? $$ f(t)=t-\frac{1}{t}, t \neq 0 $$