Question

The inflection point of the curve y = x4 − 8x3 + 24x2 + 7x − 3 is:

I've been getting confused on how to do this but I keep getting (0,3)

Answer 1

y'=4x^3-24x^2+48x+7
y"=12x^2-48x+48
set y" to zero, and solve for x

x^2-4x+4=0
(x-2)^2=0
x=2

y= use original equation to find y.

Answer 2

The response above is correct, but when you check your answer for any sign change, you'll see that at x=2, it's actually not an inflection point. The concavity does not change.

The answer is: There is no point of inflection

(at least that's the answer on apex)