Suppose h(x) = ax^3 + 11x^2. Determine a if h has an inflection point at x = 4. Show all your work.

Step-by-step explanation:

We are given the function:

And we want to determine a such that h(x) has an inflection point at x = 4.

Possible inflection points are whenever h''(x) equals 0. So, we will first differentiate h(x) twice. This yields:

So:

Inflection points occur when h''(x) = 0. So:

Since we have an inflection at x = 4:

And solving for a yields:

1,918

step-by-step explanation: