Chapter 1.2, Problem 3E

a.

To determine

To show: The first derivative of the function $f\left(x\right)=1-e^x+\left(e-1\right)\sin \left(\left(\pi /2\right)x\right)$ is zero at least once in the interval $\left[0,1\right]$ .

b.

To determine

To show: The first derivative of the function $f\left(x\right)=\left(x-1\right)\tan x+x\sin \pi x$ is zero at least once in the interval $\left[0,1\right]$ .

c.

To determine

To show: The first derivative of the function $f\left(x\right)=x\sin \pi x-\left(x-2\right)\ln x$ is zero at least once in the interval $\left[1,2\right]$ .

d.

To determine

To show: The first derivative of the function $f\left(x\right)=\left(x-2\right)\sin x\ln \left(x+2\right)$ is zero at least once in the interval $\left[-1,3\right]$ .