The local maximum of the function f(x) occurs when x=-1. Therefore, option D is the correct answer.
We need to find a local maximum of the function f(x) occurs for which x-value.
What is the local maximum of the function?
A local maximum point on a function is a point (x,y) on the graph of the function whose y coordinate is larger than all other y coordinates on the graph at points "close to'' (x,y).
Now,
The function has a value of 16 when x=-4.
When x increases to -3 the function decreases to -2.
When x increases to -2 the function increases to 0, and then a local minimum of the function f(x) occurs when x=-3.
When x increases to -1 the function continues increasing to 6.
When x increases to 0 the function decreases to 0, and then a local maximum of the function f(x) occurs when x=-1.
When x increases to 1 the function continues decreasing to -2.
Therefore, option D is the correct answer.
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