Question

For problems 8-12, use the graph of y=f(x) and the table for g(x) and g'(x) to compute the indicated derivatives. Write your final answer and only your final answer) in the space provided. Answers should be exact and fractions should be used where appropriate (do not use numbers in decimal form). 1 -4 -2 g(x) 2 5/2 3 14/5 &'(x) 7/5 1/2 1/4 -1/4 0 2 قيا 2 - 1 -2 - 1/2 4 0 5 6 8 1 6 0 2 3/2 4/5 10 4 8. Find f'(-1). 9. Find '(3) where u(x) = f(x)g(x) 10. Find k'(0) where k(x) = f(x) g(x) 11. Find (-4) where y(x) = f(g(x)) 12. Find p'(0) where p(x) = $(&($(x))) 13. Problem 13 is on the answer sheet MacBook Air

Answer 1

(3, 14) -2, 8) (12) 764,00 • Equation of line passing through (3, 4) 4 (2₂, 9) is (x-x) 9-8, 9,9) x2-x) — 9= 92-) + х,8-х, 8, x, -х Хр-х,

Using this formula, f(x) = S4x+16 if as-2 -2x+4 it -2<xel 3x-1 if 12x f'(X) = 4 if xc-2 -2 if -2<x<) if 1x (nat defined if x=-2 arx=1 3

f'(1)-2 Flo ( -2<x<1) W!(3) = f'(3)8(3)+H3) 8'(3) = (3)(2) +(8)(-2) K'(o)= 3(0).f'() - €(0)8'(0) (800)? (3)(-2) – (4) () (3) Using chain Rule, 8'() = 8'62) f'(8(x)) >> Y'(-4)= g(-4) f( 8(-4)) - (3) #2) (3)(3) Hoi -7 g ☺ - 21 5 2/3

= f'(-1) -2 12 Similarity, p'(x) = [8666m)]* •*'(844())) f'(x). 8'(46): f'(8Ctras) .: Þ'(0) = f'(6)•8' (660))• f'(946-))) = (-2)8'(4). t'(8(4)) = 62)(3)(+(-1)) 2 ☺ at x= -1 (: +(-1)= -2.4 $(4+) = -3 > f(1) = f(-17) (: f'(-3) = -3 + f(-3+) = 0) ( f discontinuan) ©& 8 Let equation of parabola is y = 1 = a (x-17² " (1,2) is vertex & symmetry about x-1=0 (13 ① at x=-3 & at x = -1

Ihlt U o $(2) = -2 passes through (-1-3) -3= 2-a (-1-1,² (y=2-2 (2-13² (-3x-11 if xs-3 it -35X<-1 2- $(x-1) 2 if sa - if x<-3 nat exist it :-3 <x<-) if x=4 (x-1) if x>-1 > $(x)= if x=-3 nat erant

. Graph of f'(x) TH S 4 3 2 » X 2 3 4 5 + - -1