A function has f''(x) = 10 and has f'(4) = 0 and f(2) = 4. Find f(x).

Answer 1

work backwards ...
f''(x) = 10
then f'(x) = 10x + c
we know that when x = 4, f'(4) = 0
0 = 10(4) + c
c=-40

so f'(x) = 10x - 40

finally , f(x) = 5x^2 - 40x + k
we know that when x =2, f(4) = 4

carry on