Find f. f ''(x) = 7 + cos x, f(0) = −1, f(9π/2) = 0. f(

f ''(x) = 7 + cos x, f(0) = −1, f(9π/2) = 0.

To find f'(x) we integrate f''(x)

f'(x) = ∫ f''(x) = ∫ (7 + cos x) dx = 7x + sin x + A

To find f'x) we integrate f'(x)

f(x) = ∫ f'(x) = ∫ (7x + sin x + A) dx = 7* - cosx + Ax + B

Now we plug in the values and solve for A and B

f(x) = - cosx + Ax + B

f(0) = −1

f(0) = - cos(0) + A(0) + B

-1 = - cos(0) + B

-1 = -1 + B

B = 0

f(9π/2) = 0

f() = - cos()+ A() + B

f() = - cos()+ A() + B

0 = - 0+ A() + 0

A() =

multiply by on both sides

A =

So f(x) = - cosx + x + 0