Suppose f(x) is positive, continuous, and f'(x) < 0 for all æ in [ – 8, 4], and| f(x)dx = 76 and L (2)dz = 21. This problem requires either exact answers, or answers rounded to at least four decimal places. Then The least possible value of ƒ( – 1) is

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A: This question is related to Functions, we will solve it using given information.

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A: Given sequence is -1             4                 -9                16              -25 By…

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A: We have to Evaluate given term.

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A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

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A: partial fraction

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A: Let's find.

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A: We have to substitution

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A: Given: We have the local maximum at the point (7, -6). So, we must have f'(7)=0. Here, f'(x) =…

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A: The function g(x,y) is defined byg(x,y) = cos(πxy) + 1log3(x-y)=cos(πxy) +…

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A: Since you have posted multiple questions i can do first question as per our company guidelines…

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A: Midpoint rule

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A: f(x)=x2+x+1f(2)=4+2+1 =7f'(x)=2x+1f'(2)=4+1 =5f''(x)=2f''(2)=2f'''(2)=0

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A: The objective of the question is evaluate the limit.

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A: We will use first shifting Theorem to solve this question.

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A: Given

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A: Given:     a) fx=4-3x ; (-1,2]           dydx=ddx4-3x                   f'x=-3   There in no…

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A: solution

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A: To find out the integration.

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