(5) Define h(x) = x³ sin for x = 0 and h(0) = 0. Show that his differentiable everywhere and that h' is continuous everywhere but fails to have a derivative at one point. You may use the rules for differentiating products, sums, and quotients of elementary functions that you learned in calculus. 6. Suppose f: (a, b) → R is differentiable at x E (a, b). Prove that

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Chapter2: Second-order Linear Odes
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Define h(x) = x³ sin for x = 0 and h(0) = 0. Show that h is differentiable everywhere and
that h' is continuous everywhere but fails to have a derivative at one point. You may use
the rules for differentiating products, sums, and quotients of elementary functions that you
learned in calculus.
6. Suppose f: (a, b) → R is differentiable at x E (a, b). Prove that
Transcribed Image Text:Define h(x) = x³ sin for x = 0 and h(0) = 0. Show that h is differentiable everywhere and that h' is continuous everywhere but fails to have a derivative at one point. You may use the rules for differentiating products, sums, and quotients of elementary functions that you learned in calculus. 6. Suppose f: (a, b) → R is differentiable at x E (a, b). Prove that
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