Question

Let f(x) be given by f(x) = x +sin(x) which is defined on [0, 2pi]. If h(x) = tan(x), find all values of x on [0,2pi] where f'(x) = h'(x).

Answer 1

Do you know how to find the derivatives?

Answer 2

If you mean the derivatives of 1+sin(x) and tan(x) then yeah, I do.

Answer 3

f'(x) = cos (x) and h'(x) = sec^2(x)

Answer 4

You set those two equations equal to each other and you can graph to find where they cross over the range given:

Use https://www.desmos.com/calculator if you dont have a calculator

Answer 5

I got sec^2(x) = cos (x) when y =1 for every 1 pi starting at 0. Thanks for your help!

Answer 6

I got x = 0 and x= 2pi as the only crossing points .... make sure you place the sec(x)^2 correctly in the calculator

Answer 7

Wait you're actually right. Thank you!