(c) h(x) = x|x|, 9. Prove that if f: R R is an even function [that is, f(-x)=f(x) for all x E R] and has a derivative at every point, then the derivative f is an odd function [that is, f'(-x) =-f'(x)...

(c) h(x) = x|x|,<br>9. Prove that if f: R R is an even function [that is, f(-x)=f(x) for all x E R] and has a<br>derivative at every point, then the derivative f is an odd function [that is, f'(-x) =-f'(x) for<br>all x E R]. Also prove that if g : R R is a differentiable odd function, then g is an even<br>function.<br>D ha defined by o(x) :=<br>xsin (1/x2) for x + 0, and g(0) := 0. Show that<br>is<br>

Extracted text: (c) h(x) = x|x|, 9. Prove that if f: R R is an even function [that is, f(-x)=f(x) for all x E R] and has a derivative at every point, then the derivative f is an odd function [that is, f'(-x) =-f'(x) for all x E R]. Also prove that if g : R R is a differentiable odd function, then g is an even function. D ha defined by o(x) := xsin (1/x2) for x + 0, and g(0) := 0. Show that is

Jun 04, 2022

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(c) h(x) = x|x|, 9. Prove that if f: R R is an even function [that is, f(-x)=f(x) for all x E R] and has a derivative at every point, then the derivative f is an odd function [that is, f'(-x) =-f'(x)...

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