Let f(t) be shown in the graph where the middle curve is a half-circle of radius 2 centered at (0,2). If X F(x) = f(t) dt, determine the following. -2 -4 -3 -2 - - 3 2 1 -2 1 2 3 5 6 (a) Find F(4). (b) Find F'(-2). (c) For x with −4 < x < 6, on which open interval(s) is the function F(x) concave down?

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A: Since you have posted a multiple question according to guildlines I will solve first(Q1)   question…

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A: Given that P(5,-2) and y=24-x the equation of the curve. Q (x, 24-x) lie on the curve.

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Q: given the following information about its derivative: f'(x) -2 f'(x) = 0 at x = -2 -10

A: We will use relation between derivative  and character of the graph to draw

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A: Graph

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Q: d. Consider the graph of y = f (x). Fill in the blanks: -3 -1

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A: is defined by .

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A: A inflection point in a graph is the point where the graph changes from concave upward to concave…

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A: we have, Differentiating w.r.t x, we getDifferentiating again w.r.t x, we getFurther,    .     .…

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A: We have to find the inflation point