Question

let f(x)=x^3+ax^2+2a^2x+a such that f(x) has a point of inflection located at x=2. What is the value of a?

Answer 1

Hint : a necessary condition for inflection point is, the "second derivative must be 0"

Answer 2

Ok so would the derivative be f'(x)=3x^2+6ax+a?

Answer 3

f(x)=x^3+ax^2+2a^2x+a

f'(x) = 3x^2 + 2ax + 2a^2

f''(x) = 6x + 2a

Answer 4

set f''(2) = 0 and solve "a"

Answer 5

ok so a is -6?

Answer 6

Yep!

Answer 7

nice! thanks a lot!

Answer 8

yw