. Homogenous Functions: A function F(x1,x2,..., tn) is homogenous of degree k if F(A¤1, Ax2,..., Aan) = X*F(x1, x2,..., Tn) for any A> 0. Prove that if F is homogenous of degree 1, then F(x1, x2,... , Tn) =F(*1,2,..., Tn) · ti

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Q: If f(x) is continuous, f(-1) = 2, and f(2)= -1, then f(x) has a root in [-1,2].

A: Given:  fx is continuous , f-1= 2, f2 = -1  To Prove:  fx has a root in -1,2

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A: Definition:

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A: We explain mean value theorem example.

Q: 5. Suppose f(x) is an odd function. Prove that g(x)=f(x)| is an even function.

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A: Or

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A: The given statement is true .

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A: graph

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A: fx=2xgx=x            if x is even2x-1     if x is odd

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A: We have to conclude about local extreme value of f from the graph.

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