Provide an appropriate response.Graph f(x) = (x - 5)2ex and its first derivative together. Comment on the behavior of f in relation to the signs and values of f' Identify significant points.

Question

What will be an ideal response?

Answer 1

f'(x) = ex(2(x - 5) + (x - 5)2). f'(x) = 0 at x = 3 and at x = 5. This is when the local min and local max of f(x) occur. Initially the function is increasing and f'(x) is positive. It becomes negative at the same point that f(x) begins decreasing. It again becomes positive at the same point that f(x) begins increasing again.