Question

For f(x) = esin(x) use your graphing calculator to find the number of zeros for f '(x) on the closed interval [0, 2Ď€].

Answer 1

The given function is

f(x) = esin(x)

We have to find the zeros for f '(x) in the given interval [0, 2Ď€]

So for the given function, we have

f '(x) = ecos(x)

For zeros, let

f '(x) = 0

ecos(x) = 0

cos(x) = 0

So the required zeros are

x = π/2  and x = 3π/2

And if the interval is not bounded above, then we can have

x = nπ/2 , where n ∈ Z