Suppose f (x) is a function defined on the interval [0, 6] and whose graph consists of a circular arc and two line segments as shown in the graph below.

g(x) = ∫0 x f(t)dt.

Find the absolute minimum value for g(x) on the interval [0, 6]. Show the analysis (evaluate the critical points) that leads to your answer.

http://curriculum.kcdistancelearning.com/courses/CALCABx-AP-A09/b/assessments/Unit5_ExamFR/Unit5_ExamFR_1q2.jpg

Question

Suppose f (x) is a function defined on the interval [0, 6] and whose graph consists of a circular arc and two line segments as shown in the graph below. 

g(x) = ∫0 x f(t)dt. 

Find the absolute minimum value for g(x) on the interval [0, 6]. Show the analysis (evaluate the critical points) that leads to your answer.


http://curriculum.kcdistancelearning.com/courses/CALCABx-AP-A09/b/assessments/Unit5_ExamFR/Unit5_ExamFR_1q2.jpg

anonymous · Answer

the minimum value of the integral?

anonymous · Answer

the integral is giving you the area, except that the area below the curve is negative
therefore the minimum value will be at 5 since that includes all the negative area you are going to get

anonymous · Answer

if you want to please the instructions, note that the derivative of the integral is the integrand (the picture in this case) and it has two zeros, one at 2 and one at 5
but that is kind of silly

anonymous · Answer

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