If f has a local maximum value at x = a, what would you expect the graph of f ' to look like near x = a?

the graph of f ' should be above the x-axis, cross the x-axis at x = a, and go below the x-axis as x increases.
the graph of f ' should be below the x-axis, cross the x-axis at x = a, and go above the x-axis as x increases.
the graph of f ' should be positive and increasing as x approaches a.
the graph of f ' should be negative and increasing as x approaches a.
the graph of f ' should be negative and decreasing as x approaches a.

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.

1.true 2.false? ? i think. .

step-by-step explanation: