4.3 The Chain Rule 1. {Algebra review} Let f(x)=2x²-5 x and g(x)=6x+2. Find f[g(−5)]. 2. {Algebra review} Write h(x)=√√8x-3 as the composite of two functions f(x) and g(x). (There may be more than one way to do this.)

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A: We need to find (h∘g∘f)(1) i.e., h(g(f(1)))Step 1: Compute f(1)f(x) = -5x - 1 f(1) = -5(1) - 1 f(1)…

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A: f(x)=9x2−xg(x)=(5x−7)9Quotient rule states thatf′(x)=d/dx[​(9x2−x)]= 18x−1g′(x)=9(5x−7)8⋅5=…

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A: f(g(−2))=−4g(f(1))=−2f(f(2))=−1g(g(−3))=−3

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Q: Total marks 15 4. : Let f R2 R be defined by f(x1, x2) = 2x²- 8x1x2+4x+2. Find all local minima of f…

A: Step 1: Compute the partial derivatives fx1​​=∂x1​∂f​=4x1​−8x2​fx2​​=∂x2​∂f​=−8x1​+12x22​Step 2:…

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Q: g Ske Find the area of the region bounded by the parabola x = 2y- y² + 1 and the line y = x + 1

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

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Q: Please help on both Part b) and c) below Thanks

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Q: Good Day, Kindly assist me with the following query. Any assistance would be appreciated.

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