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Given the following functions, find the difference Quotient and using the difference Quotient, derive the derivative in each case. a. Y=f(x)=3x^2 b. Y=f(x)=5x^3 c. Y=f(x)=3x^2 + 6x^3 d. Y=f(x)=3x^2 -x^4 Show that the Taylor expansion leaves the functions unchanged. a. Y=f(x)=3x^2 b. Y=f(x)=6x^3 Given the following, find the optimum and show if the optimum is a maximum or minimum . a. Y=f(x, z) = -2x^2 + xz - z^2 b. Y= f(x, z) = x^2 +4xz + 2z^2
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