find function

Question

Find a function f'(x)=8e^x-9x and f(0)=3

 

f(x)= ?

Answer 1

OK, with the edited information:

 

f'(x) = 8e^x - 9x

f(0) = 3

 

f(x) = ∫f'(x)dx = 8e^x - 9x²/2 + c

 

f(0) = 3 ⇒

 

3 = 8e⁽⁰⁾ - 9(0)²/2 + c = 8 + c

 

c = 3 - 8 = -5

 

f(x) = 8e^x - 9x²/2 - 5

Answer 2

Take the anti-derivative of f'(x).

 

f(x) = 8e^x - (9/2)x² + C

 

 

Now Set f(x)=3   and x=0.  This will allow you to solve for C.

 

3 = 8 + C

 

-5 = C