Question

suppose f^n (x)= -36 sin(6x) and f'(0)=6 and f(0)= -5

f(π /4)= ?

Answer 1

To find f(π/4), we need to integrate f'(x).

Since f'(0) = 6, we can find f(x) by integrating this derivative:
f(x) = ∫6 dx = 6x + C

Using the information that f(0) = -5, we can solve for C:
-5 = 6(0) + C
C = -5

So, f(x) = 6x - 5.

Now, let's find f(π/4) using this equation:
f(π/4) = 6(π/4) - 5
f(π/4) = 3π/2 - 5