Chapter 3.3, Problem 5ES

Determine whether the function $f$ is one-to-one by examining the sign off $f^{\prime }\left(x\right)$ .

(a) $f\left(x\right)=x^2+8x+1$

(b) $f\left(x\right)=2x^5+x^3+3x+2$

(c) $f\left(x\right)=2x+\sin x$

(d) $f\left(x\right)={\left(\frac{1}{2}\right)}^x$