SOLUTION: f''x=3x^2-5 sin x+2e^x, f'(0)=10 and f(0)=0 what is f(x)?

Algebra ->  Equations -> SOLUTION: f''x=3x^2-5 sin x+2e^x, f'(0)=10 and f(0)=0 what is f(x)?      Log On


   

Question 1026683: f''x=3x^2-5 sin x+2e^x, f'(0)=10 and f(0)=0 what is f(x)?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
f"(x) = 3x%5E2-5sinx%2B2e%5Ex
==> f'(x) = x%5E3%2B5cosx%2B2e%5Ex%2Bc for some constant c.
f'(0) = 10 ==> 10+=+0%5E3%2B5cos0%2B2e%5E0%2Bc ==> c = 3.
==> f'(x) = x%5E3%2B5cosx%2B2e%5Ex%2B3
==> f%28x%29+=+x%5E4%2F4+%2B+5sinx+%2B+2e%5Ex+%2B+3x+%2B+k for some constant k.
f(0) = 0 ==> f%280%29+=+0%5E4%2F4+%2B+5sin0+%2B+2e%5E0+%2B+3%2A0+%2B+k+=+0 ==> k = -2.
highlight%28f%28x%29+=+x%5E4%2F4+%2B+5sinx+%2B+2e%5Ex+%2B+3x+-+2%29