Question

Hey everyone!! please help..

Find a function f such that the graph of f has a horizontal tangent at (1,0) and
f"(x)=10x??

Thanks

Answer 1

if f '' (x) =10x
then f ' (x) = 5x^2 + c
but at (1,0), f ' (x) = 0
0 = 5(1) + c
c = -5
so f ' (x) = 5x^2 - 5

f(x) = (5/3)x^3 - 5x + k
but (1,0) lies on it
0 = (5/3)(1) - 5 + k
k = 5 - 5/3 = 10/3

f(x) = (5/3)x^3 - 5x + 10/3