Question

f(x) = 4x^4 − 32x^3 + 89x^2 − 95x + 33
find the inflection points.

Answer 1

Can you just graph it on your calculator or do you want to analyze the function?

Answer 2

analyze the function

Answer 3

Well 89 is prime, 95 and 33 don't have common factors. 4 and 32 do.. Factor right?

Answer 4

Do you know about critical points?

Answer 5

At point of inflection f"(x)=0 or does not exist..

Answer 6

\[f(x)=4x^4-32x^3+89x^2-95x+33\]
you need to find concavity for this
\[f'(x)=16x^3-96x^2+178x-95\]
\[f''(x)=48x^2-192x+178\]
\[48x^2-192x+179=0\]
\[x=2\pm\frac{\sqrt{\frac{13}{3}}}{4}\]

Answer 7

So I think you are correct