Question

11.1 Use the four step process to find the derivative of f(x) = -4r? - 2x +3. (a) Find f(x+h) (b) Find f(x+h)-f(x) (c) Find $(2+ h) – f(x) (d) Find lim f(x+h)-f(2) h-10 11.2 Use the rules to find the derivatives of the following functions. (a) f(x) = 212 (b) f(x) = .24x1/2 (c) f(x) = 134. (d) f(x) = 420-1 (e) f(x) = -.02.2 + 45x - 200.

Answer 1

Given f(x1=-4% - 2x +3. fath? = - 4(x+h) = 2(a+h) +3 = -4 (arzach tu)-2a-2ht3 = (-4-8ahahh=2x-2h+3) (rear) o fath)-from 1 © =(-40%8ah-45 - 20-2h+3) -(-407-2013) = (68xhauñozh) (reqi) forth) -Hes $Xh4h-2h) [fony = (-80 - 4h-2) ((rea) ( provided h=0) @ hotel yang teeth) fres (-fenye =680-2) = F264241) (129)

in derivative of flor-45_2243 in = 2(4x+)] (oreq.) (11.2) - Giren fag=021 25. Th, Jц% ) - Ry = 0.27 (reth) 5 -0.21% = 0.21 [ +5 ahh tlo x3ht 1oxh? + 5.anthenol uning binomial theorem (ntyna" the xhly't had hy t...ty") = 0.21 h 584flox3h tour +50h the 7 --- - derivative of flaj in f'(x) = lim feath) & Hx) huyo h a dim 0.21 h [sa Hou?htlo xhtsan the 7 hto. b . = lim 0.21 [ 54% + 1x² + loath + 5xhthy]

[:hto, conto] = 0.21 x [5 xy +o] 1.') = 1.0529 (req.) 11.2 a - Here f(x) = 0.24 h An before tas - lim feath feaths - fins t = h to L 0.24 cath) - 0.240 = nim rath - Cod a a (orzy). Lindo reth -(0.24). The more l'ho Trath treh hura) (Withtun)

= (o.ny). dim ho 4th- Truth of high carb) (ath)= a by = (0.24 ) im Florzy) vatra (0.2).sta: IT into) if(x1=16.121/621)