Evaluate g (-2), g (2), g (0), g (3). On what x-interval(s) is g increasing? (us

Question

Evaluate g (-2), g (2), g (0), g (3).

On what x-interval(s) is g increasing? (use interval or inequality notation)

What are the maximum and minimum values of the function g over [-2,3]?

Explanation / Answer

g(-2) = integral of h(t)dt from -2 to -2 which is nothing but area formed from h(t) from -2 t0 -2 which is equal to 0 =>g(-2) =0 g(2) = integral of h(t)dt from -2 to 2 which is nothing but area formed by h(t) from -2 to 2 =1/2*2*2 - 1/2*2*2 =0 g(0) = integral of h(t)dt from -2 to 0 which is nothing but area formed by h(t) from -2 to 0 = 1/2*2*2 = 2 g(3) = integral of h(t)dt from -2 to 3 which is nothing but area formed by h(t) from -2 to 3 =1/2*2*2-1/2*2*2 +1/2*1*2 =1 maximum value of the function is 2 which comes at 0 minimum value of the function is 0 which comes at -2,2

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