calculus (point me in the right direction please?)
posted by andy
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)?

ahmad
f'= 3x2 + 8x
f'(5)= 3(25) + 8 (5)=
=75+40=115
so u replace x by 5 in fx and u substract 
andy
but how would you get f(5)?

Damon
Use 5 for x
5^3 + 4(5)^2 = 125 + 100 = 225 
Steve
?? if we use f'(x) = 3x^2 + 8x, then that means
f(x) = x^3 + 4x^2 + ∫[0,x] (xt)(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?
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