SOLUTION: A1. Consider the function {{{f(x)=x^2*e^(-x)^2}}}.
a. Determine the critical points of f.
b. Determine the absolute maximum and absolute minimum values of f on the interval[-2, 2
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-> SOLUTION: A1. Consider the function {{{f(x)=x^2*e^(-x)^2}}}.
a. Determine the critical points of f.
b. Determine the absolute maximum and absolute minimum values of f on the interval[-2, 2
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Question 1041435: A1. Consider the function .
a. Determine the critical points of f.
b. Determine the absolute maximum and absolute minimum values of f on the interval[-2, 2]
A2. Suppose that f is a polynomial of degree n, where n ≥ 2. Show that if f has n distinct roots, then must have distinct roots.
A2. Suppose that is a polynomial of degree , where . Show that if has distinct roots, then must have distinct roots.
Between any two roots of there must be a root of by Rolle's Theorem. But since all roots of are distinct and since is perforce of degree , there can only be roots of and they must be distinct.
John
My calculator said it, I believe it, that settles it
