Chapter 2, Problem 11RE

The accompanying figure shows the graph of $y=f\text{'}\left(x\right)$ for an unspecified function $f$ .

(a) For what values of $x$ does the curve $y=f\left(x\right)$ have a horizontal tangent line?

(b) Over what intervals does the curve $y=f\left(x\right)$ have tangent lines with positive slope?

(c) Over what intervals does the curve $y=f\left(x\right)$ have tangent lines with negative slope?

(d) Given that $g\left(x\right)=f\left(x\right)\sin x$ , find $g^{″}\left(0\right)$ .