6 Suppose that a function h satisfies –x² < h(x) < x² for all x. Prove that h is differen- tiable at x = 0 and that h'(0) = 0.

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A: Solution is given below..

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A: Given statement

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A: Explanation of the answer is as follows

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A: We will use Newton's method of optimization to find the maximum value of f(x)

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A: .Given,f(x,y) = (2x4+y4) ey2x +x y3Put y= xSo we get,f(x,x)= (2x4+x4) ex2x +x x3 f(x,x)= (3x4) e0.5…

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