Question

Consider the graph of the function g shown below. The domain of g is [0,10], and the graph of g is comprised of two line segments and a quarter circle.

1. The function F is defined on [0,10] . It is an antiderivative of g and satisfies F(7)=0. Sketch a graph of F

2. Use your knowledge of area to compute F(4). Explain your reasoning.

3. Write a formula for F using an appropriate integral of g.

4. The function G is defined on [0,10] . It is an antiderivative of g and satisfies G(0)=-2. Sketch a graph of G

5. Compute G(3) and G(10)

6. Compare and contrast the graphs of F and G.

I guess I can do the rest by myself if I can figure out how to do 1 and 3. I just can't think of a way to find an antiderivative from the given graph and draw it.

Thank you for your help.

Answer 1

6(48) (8,8) 8 (6 (106) A6 10 4 egn of line AB: 8-6 ay-6= y = x+6, okay 4-o egn of line Be: - - y = 8, 48 x egn of curre co:- (x-8) ² - ( 8-6) ² = 2² (4-6) ² = (x-8) ² - 2 2 (4-6) 2 = x² - 16x +60 . 4-6 = + (x²16x+60 y = 6 + (x²-16x + 60 gry 6, for this curre. y = 6 + x²-16x+60 8x210

8 x2 44 X 48 6+3824-16x+60, 8

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