calculus (point me in the right direction please?)

f(x) and f′(x) are continuous, differentiable functions that satisfy

f(x)=x^3+4x^2+∫(from 0 to x)(x−t)f′(t) dt.

What is f′(5)−f(5)?

asked by andy
  1. f'= 3x2 + 8x
    f'(5)= 3(25) + 8 (5)=
    =75+40=115

    so u replace x by 5 in fx and u substract

    posted by ahmad
  2. but how would you get f(5)?

    posted by andy
  3. Use 5 for x
    5^3 + 4(5)^2 = 125 + 100 = 225

    posted by Damon
  4. ?? if we use f'(x) = 3x^2 + 8x, then that means

    f(x) = x^3 + 4x^2 + ∫[0,x] (x-t)(3t^2+8t)
    = 1/4 x^4 + 7/3 x^3 + 4x^2

    but then f'(x) = x^3 + 7x^2 + 8x

    Am I missing something?

    posted by Steve

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