discussion4 - Math 21A Kouba Discussion Sheet 4 1 Use the...

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Unformatted text preview: Math 21A Kouba Discussion Sheet 4 1.) Use the limit definition of derivative to compute f’(a:) for each of the following functions. a.) me) = 3+1”; b.) me) = $211 c.) f(x) : sin3m d.) ms) = W 2.) Use any method to differentiate each of the following functions. a.) y=1+5x—6a:5 b.) f(m) = 1:3 sins: C) __ m+5 'yfixztana: 13 C081) d«) 9(x) = tanm — 5secx 3.) Determine a function whose derivative is : a.) f’(x) = 1 + 53: — 69:5 b.) was) = 4 — «5 2 2: +1 c.)y’= m2 (my/Z 4x3+3x2+2x+1 x4+m3+x2+x+1 4.) Use the limit definition of derivative to show that f = is NOT differentiable at a: = 0, i.e., show that f’(0) does not exist. 5.) Use the limit definition of derivative to show that the following function IS differentiable at a: = 1, i.e., show that f’(1) does exist. 2+fi, ifcml f(m):{1 5 5334—5, 6.) Draw a possible graph for f’ using the given graph of y : f 7.) Let f(x) = :c-vaules ? m2: 1. Slove f’ = 0 for :13. What is the geometric significance of these 8.) Assume that h(m) = f(a:)g(m) and that f(0) = 1, f’(0) = 2, g(()) = —1, and g’(0) = 3. Determine the value of h’ (0) +++++++++++++++++++++++++++++++++++++++++++ The following problem is for recreational purposes only. 9.) A snail is at the bottom of a well which is 100 feet deep. Each day it climbs up 5 feet and back down 4 feet. In how many days will the hapless snail reach the top of the well ? ...
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discussion4 - Math 21A Kouba Discussion Sheet 4 1 Use the...

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