2.4

10. 6/(9t+2)^1/3 worked by Nolan Blair Correct! checked by C ﻿L I ﻿N T Patterson 11. F(t) = Sq. 1-t (1-t)^1/2 1/2(1-t)^-1/2 * (-1) = -1/2(1-t)^1/2 Worked by Heather Anderson -Correct! Checked by Warner Boin

15. y=2(4th square root 4-x^2) y'= 2(1/4)(4-x^2)^-3/4(-2x) = -x/4th square root (4-x^2)^3

Worked by Jackson Hart Checked by Anthony Lukefahr

21. Worked by Warner Boin

23) F(x) = x^2(x-2)^4 = x^2[4(x-2)^3 x (1)] + 2x(x-2)^4 = x^2[4(x-2)^3] + 2x(x-2)^4 Worked by Thomas Sturm

53. 1/4 sin^2 2Theta 1/4(sin2theta)^2 2(1/4)(sin2theta)(cos2theta)(2) sin2thetacos2theta 1/2sin4theta worked by sophia Lamay checked by Abby Newton

59. (t^2+2t+8)^1/2 1/2(t^2+2t+8)^-1/2 * 2t+2 1/2(t^2+2t+8) ^1/2 *2t+2 Points (2,4) plug in the x value 2 Worked by Rachel Rilling Correct, Checked by Marla Roper

67. f(x)=sqrt(3x^2-2) =(3x^2-2)^(1/2) f'(x)=[1/2(3x^2-2)^(1/2)][6x] =3x/(3x^2-2)^1/2 f'(3)=3(3)/[3(3)^2-2]^1/2 =9/5 y-5=9/5(x-3) 5y-25=9(x-3) 0=9x-5y-2 Worked by Neil Klenk =Correc t Checked By JOey Cahill =

83) f(x)=2(x^2-1)^3 f '(x)=6(x^2-1)^2(2x) f '(x)=12x(x^4 -2x^2 +1) f '(x)=12x^5-24x^3+12x f (x)=60x^4-72x^2+12 f (x)=12(5x^2-1)(x^2+1) worked by Layne Miller Correct, checked by Hayley Linton

91) As F reaches a horizontal tangent line, F' has a zero at that point. 92) I don't know how to start the problem. worked by:Zarion Hilaire Checked by: Houston Spence # 91 is correct. I dont know how to do #92 too.

Worked by Kendall Jones

97) a- f '(5)= (-3)(-2)+(6)(3) =25 b- f ' (5)= g ' (3)(-2) = 2g ' 3 c- f ' (5)= (3(6)- (-3)(-2)) / (3)^2 =4/3 d- f ' (5)= 3(3)^2(6) =162 Worked by Michelle Tassin Checked by Hannah Mozafari- Correct!