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00fall-minitest3 - f, g : [ a, b ] 7 R are dierentiable and...

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MAT 371 Advanced Calculus / 50 Nov 14, 2000 Minitest 3 name 1 . State the standard definition for differentiability of a function at a point. 2 . Suppose f : [ a, b ] 7→ R is differentiable on [ a, b ]. Prove that f is continuous on [ a, b ]. 3 . Suppose f, g : [ a, b ] 7→ R are differentiable on [ a, b ]. Prove that f · g is continuous on [ a, b ]. 4. a . State the mean value theorem (MVT). b . Suppose
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Unformatted text preview: f, g : [ a, b ] 7 R are dierentiable and f > g . Use the MVT to prove that there exists at most one point x [ a, b ] such that f ( x ) = g ( x ). Bonus : Give an example of a function that is dierentiable everywhere, but whose derivative is not continuous. Prove that you are correct....
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