Question

Let f(x) = cos(x) + 2x. Where does f have critical points?

Answer 1

Answer:

f has no critical points.

Step-by-step explanation:

We are given:

$f(x)=\cos(x)+2x$

A function has critical points whenever its derivative equals 0 or is undefined.

Differentiate the function:

$f'(x)=-\sin(x)+2$

Since this will never be undefined, solve for its zeros:

$0=-\sin(x)+2$

Hence:

$\displaystyle \sin(x)=2$

Recall that the value of sine is always between -1 and 1.

Thus, no real solutions exist.

Therefore, f has no critical points.