SOLUTION: If f ′(x) = −7 x−3 and f(0) = −5, find f(x). I think I get the basic, but can someone explain with steps?

Algebra ->  Functions -> SOLUTION: If f ′(x) = −7 x−3 and f(0) = −5, find f(x). I think I get the basic, but can someone explain with steps?      Log On


   

Question 972417: If f ′(x) = −7 x−3 and f(0) = −5, find f(x).
I think I get the basic, but can someone explain with steps?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
If f'(x) = −7 x−3 and f(0) = −5, find f(x)
.
Start by finding the "indefinite integral" of
f'(x) = −7 x−3
f(x) = (-7/2)x^2 - 3x + C
now we use f(0)=-5 to find C
-5 = (-7/2)(0)^2 - 3(0) + C
-5 = C
therefore:
f(x) = (-7/2)x^2 - 3x - 5