91Ó°ÊÓ

Use any method to find the relative extrema of the function \(f\). $$f(x)=x^{2} e^{x}$$

Give a complete graph of the function, and identify the location of all relative extrema and inflection points. Check your work with a graphing utility. $$x+\sin x$$

Use any method to find the relative extrema of the function \(f\). $$f(x)=\left|x^{2}-4\right|$$

In each part, assume that \(a\) is a constant and find the inflection points, if any. (a) \(f(x)=(x-a)^{3}\) (b) \(f(x)=(x-a)^{4}\)

Give a complete graph of the function, and identify the location of all relative extrema and inflection points. Check your work with a graphing utility. $$x-\cos x$$

Use any method to find the relative extrema of the function \(f\). $$f(x)=\left\\{\begin{array}{ll} 9-x, & x \leq 3 \\\x^{2}-3, & x>3\end{array}\right.$$

Find the relative extrema in the interval \(0

Give a complete graph of the function, and identify the location of all relative extrema and inflection points. Check your work with a graphing utility. $$\sin x+\cos x$$

If \(f\) is increasing on an interval \([0, b),\) then it follows from Definition 5.1.1 that \(f(0)0,\) and confirm the inequality with a graphing utility. [Hint: Show that the function \(\left.f(x)=1+\frac{1}{3} x-\sqrt[3]{1+x} \text { is increasing on }[0,+\infty) .\right]\)

Give a complete graph of the function, and identify the location of all relative extrema and inflection points. Check your work with a graphing utility. $$\sqrt{3} \cos x+\sin x$$