How many critical points: cosine function

Question

The derivative of a function g is given by,

g'(x) = cos((x-pi/2)^x)

How many critical points does the function have on the interval [1.8, 3.7]?

A. 0

B. 3

C. 5

D. 6

Answer 1

As written your problem wants the solution of log (π/2)=x log(x-(π/2)) which is approximately 2.75. That is there is 1 critical point in the given interval.

But 3π/2 and 5π/2 will also give x values in the interval. That means there are 3 critical points in the required interval.

In light of Doug C.'s comment I went to look at Desmos also.

I agree with him...there are 5 for x=1, 3, 5, 7, and 9 times pi.

I got lazy and didn't run my calculations beyond 5 pi.