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:

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation:

step-by-step explanation:

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