Find a function

Question

Find a function f(x) such that f'(x)=-9e^x-8x and f(0)=-2

f(x)=

Answer 1

Paul integrated correctly but solved for C improperly, as e^0 = 1.

f(x)=-9e^x - 4x² + C, so f(0) = -9*1 - 0 + C = -9 + C

-9 + C = -2

C = -2 + 9

C = 7

f(x)=-9e^x - 4x² + 7

Answer 2

f(x)=-9e^x - 4x² + C

You determine C from the initial condition: f(0)=C=-2.