MIT18_014F10_pset6

# MIT18_014F10_pset6 - Bonus Prove a pseudo-converse to(4 In...

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Derivatives Pset 6 Due October 22 (4 points each) (1) page 181:25 (2) page 186:4. Note that x 2 / 3 = ( 3 x ) 2 , and recall we determined how to take this derivative for x < 0 because the root was odd. (3) page 191:9 (4) Suppose that f is diﬀerentiable at x = c . Show that | f | is diﬀerentiable at x = c provided f ( c ) = 0. Give a counterexample when f ( c ) = 0. (5) Let f ( x ) = xg ( x ) where g is a continuous function deFned on [ 1 , 1]. Prove that f is diﬀerentiable at x = 0 and Fnd f (0) in terms of g . (The hardest part of this problem will be writing all of the details very carefully. Justify your equalities.) (6) page 208:18

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Unformatted text preview: Bonus: Prove a pseudo-converse to (4). In particular, prove that if | f | is diﬀeren-tiable at x = c and f is continuous at x = c , then f is diﬀerentiable at x = c . 1 MIT OpenCourseWare http://ocw.mit.edu 18.014 Calculus with Theory Fall 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
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MIT18_014F10_pset6 - Bonus Prove a pseudo-converse to(4 In...

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