Question

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1. Find the derivative of each of the following unctions: (e) w- 4u/2 (f) w=4u1/4 12 (c) y7x (b) y 63 2, Find the following: 0 (b) -9x1/3 (-oub du 3. Find f(1) and f(2) from the following functions: (C) f(x)--5x-2 (d) f(x)- ^*4/3 (a) y- f(x) -18x 4. Graph a function f(x) that gives rise to the derivative function f'(x) 0. Then graph a function 9(x) characterized by g(xo)0

Answer 1

(a) y = x^12 dy/dx = d/dx (x^12) = > 12 x^12 - 1 12 x^11 (b) y = 63 dy/dx = d/dx (64) = 0 (zero) (c) y = 7 x^5 dy/dx = d/dx (7 x^5) = 35 x^4 (d) w = 3 u^1 dw/du = d/du (3 u^1) = 3 u^1 - 1 = > 3 (e) w = -4 u^1/2 dw/du = d/du (- 4 u^1/2) - 4 x1/2 u^1/2 - 1 - 2 u^- 1/2 (f) w = 4 u^1/4 4^1 times 1/4 times u^1/4 - 1 u^- 3/4 (a) d/dx (- x^- 4) = > - 1 times (- 4) times - x^-4 - 1 4x - x^-5 (b) d/dx (9 times 1/3) = > 9 times 1/3 times x^1/3 - 1 3 x^- 2/3 (c) d/dw (5 w^4) = 5.4 w^4 - 1 = > 20 w^3 (d) d/dx (c x^2) = 2 middot C middot x^2 - 1 2 cx