2.2+pg+115

1b. (1,1) y=x^3 x^3 = 3x^2 3*(1)^2= 3 Worked by Will Owen

3.y=8 y=0 worked by dingleberry good CHECKED BY HOUSTON

5. y=x^6 y'=6x^5 worked by emily othold correct checked by aaron henderson

worked by Zarion Hilaire checked by dingleberry

7. y= 1/x^7 //change to// x^-7 y^1= -7x^-8 //change to// -7/x^8 Worked by Abby Newton correct, checked by hayley linton

11. f(x)=x+1 f ' (x)= lim as x-->0 (x+1+delta x)-(x+1)/ delta x every thing cancels out and there is a remaineder of 1 answer: 1 worked by Alex Stevens Checked by Thomas Sturm

13. f(t)= -2t^2+3t-6 -2(2)t+3t f^1(t)= -4t+3t Worked by Abby Newton (can this still count as checked?) checked by sophia lamay?

15.) y=x^2+4x^3 2x+12x^2 worked by Will McCrocklin

16) y= 8-x^3 = 1-3x^2

Worked and Checked by Krissy Denby

17. (3t)^2-2 worked by aaron henderson checked by Bryan Rucker

19. (Pi/2)sin(theta) – cos(theta)

Sin(theta) = cos(theta) Cos (theta) = -sin(theta)

Answer) (Pi/2)cos(theta) + sin (Theta) Worked by Clint Patterson 21.worked by Zarion Hilaire checked by hannah Smythe 23. (-1/x^2)-3cosx worked by aaron henderson Checked by Bryan Rucker

25. y=5/2x^2 rewrite: 5*x^2/2 differentiate: -5*5*x^-3/3 simplify: -25x^-3/3

Worked by Maelle Grenier Checked by Clint Patterson

26. Worked by Hayley Linton checked by sophia lamay

27. y= 3/(2x)^3 REWRITE DIFFERENTIABLE SIMPLIFY 3 (x^3)/2 -3 X 3 X x ^ -2/2 -9x^-2/2 = -9/2x^2

WORKED BY HOUSTON SPENCE correct checkd by will mccrocklin

29. y= sqrt. x/4 y=x^(1/2)/4: rewrite =(1/4)x^(1/2) =(1/8)x^(-1/2):differentiate =1/8x^(1/2):simplify worked by emily othold Correct! checked by Ellen Wagner

35. y=(2x+1)^2 (0,1) y=(4x^2)+4x+1 y'=8x+4 y'=8(0)+4 y'=4 worked by drew galbraith

39. d/dx(x^2) = 2x d/dx(5) = 0 d/dx(3x^-2) = 1/6x f'(x) = 2x + 1/6x = 13/6x Worked by Will Morisseau correct checked by Nadia Guillen

43. F(x)= (x^3-3x^2+4)/x^2 F(x)= x-3+4x^-2 F'(x)= (1)-(8/x^3) F'(x)= (x3-8)/x^3 Worked by ERIN RANDALL

49. 4/5s^(1/5) - 2/3s^(1/3)

Worked by daniel benoit Checked by Maelle Grenier

53. Worked by Olga Tobias

57) y=x^4- 8x^2+2 f'(x)=4x^3-16 4x(x^2-4) 4x=0 (x+2)= -2 (x-2)= 2 plug in x factors into y=x^4- 8x^2+2 Answer: (0,2) (-2,-14) (2,-14) Worked by Hannah Mozafari

61. Y1= 1+cosx cosx=-1 x=pie At x+pie y=pie (pie, pie) Worked by Brice Simpson Checked by Hannah Mozafari: Correct!

Worked By Elborz Safarzadeh

67) worked by Jane Swanson Correct! Checked by Krissy Denby 72) f(x) because if you take the derative of of a parabola you would get that x^2, which is a straight line worked by sunny krishnan Correct checked by Louis Ortizzz

89) avg. rate of change f(t)=2(x)+7 f(1)= 2(1)+7=9 f(2)=2(2)+7=11 slope- y2-y1/x2-x1=2 (average rate of change) derivative= 2 linear function because derivative is two, no matter what you plug in for x derivative will always be 2 instantaneous rate of change= 2 same as slope for average rate of change for these end points the derivative and average rate of change are equal. worked by sunny krishnan

correct!! checked by Jane Swanson

92) sin x when f(0) = (0,0) when f( pi /6) = ( pi /6, 1/2) Rate= (.5-0) / (( pi /6) - 0) = .5/ pi/6 = 3 / pi Worked by Connor Smith