Assume g: [0, 8] → R is a continuous function for which: on the intervals [0, 3) U (5, 8], the values of g(t) are positive; on the interval (3,5), the values of g(t) are negative. Also, let function A: [0, 8] → R be defined by A(x) = g(t) dt. A. The function A is increasing on the intervals [0, 3] U [5, 8] and decreasing on the interval [3, 5]. Explain this statement both geometrically (thinking in terms of the signed area between the graph of function g and the horizontal axis) and algebraically (using the first fundamental theorem of integral calculus. B. If the maximum value of function g is 10 and the minimum value of function g is -6, then the maximum value of function A must be less than 60 and the minimum value of function A must be greater than-12. Explain.
Assume g: [0, 8] → R is a continuous function for which: on the intervals [0, 3) U (5, 8], the values of g(t) are positive; on the interval (3,5), the values of g(t) are negative. Also, let function A: [0, 8] → R be defined by A(x) = g(t) dt. A. The function A is increasing on the intervals [0, 3] U [5, 8] and decreasing on the interval [3, 5]. Explain this statement both geometrically (thinking in terms of the signed area between the graph of function g and the horizontal axis) and algebraically (using the first fundamental theorem of integral calculus. B. If the maximum value of function g is 10 and the minimum value of function g is -6, then the maximum value of function A must be less than 60 and the minimum value of function A must be greater than-12. Explain.
Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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![2. Assume g: [0, 8] → R is a continuous function for which: on the intervals [0, 3) U (5, 8], the values of g(t) are positive; on the interval (3,5), the values
of g(t) are negative. Also, let function A: [0, 8] → R be defined by A(x) = fő g(t) dt.
A. The function A is increasing on the intervals [0, 3] U [5, 8] and decreasing on the interval [3, 5]. Explain this statement both geometrically (thinking in
terms of the signed area between the graph of function g and the horizontal axis) and algebraically (using the first fundamental theorem of integral
calculus.
B. If the maximum value of function g is 10 and the minimum value of function g is -6, then the maximum value of function A must be less than 60 and
the minimum value of function A must be greater than -12. Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0724d636-1660-41e9-be6d-29c03d60387f%2F5ed2a58e-3b38-417c-a166-4af75a8cc5d6%2Fn9fshch_processed.png&w=3840&q=75)
Transcribed Image Text:2. Assume g: [0, 8] → R is a continuous function for which: on the intervals [0, 3) U (5, 8], the values of g(t) are positive; on the interval (3,5), the values
of g(t) are negative. Also, let function A: [0, 8] → R be defined by A(x) = fő g(t) dt.
A. The function A is increasing on the intervals [0, 3] U [5, 8] and decreasing on the interval [3, 5]. Explain this statement both geometrically (thinking in
terms of the signed area between the graph of function g and the horizontal axis) and algebraically (using the first fundamental theorem of integral
calculus.
B. If the maximum value of function g is 10 and the minimum value of function g is -6, then the maximum value of function A must be less than 60 and
the minimum value of function A must be greater than -12. Explain.
Expert Solution
Step 1
Given: is a continous function for which on the intervals , the values of are positive; on the interval , the values of are negative.
Also, be defined by .
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