15. [-/0.25 Points] DETAILS SCALC ET8 3.1.064. MY NOTES ASK YOU R TEACHER Find equations of both lines through the point (2, 73) that are tangent to the parabola y = X2 + X. y = (smaller slope) y = (larger slope) 16. [-/0.25 Points] DETAILS SCALCET8 3.1.069. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find a cubic function y = ax3 + bx2 + or + d whose graph has horizontal tangents at the ponnts (2, 5) and (2, 1). y: Need Help? 17. [-/0.25 Points] DETAILS SCALCET8 3.1.070. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find a parabola win equation y : ax2 + bx + c that has slope 11 at x : 1, slope 17 atx : l, and passes through the point (1, 11). y: 18. [-/0.25 Points] DETAILS SCALCET8 3.1.077. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER For what values ofa and b is the line 5x + y = b tangent to the parabola y = ax2 when x = 2? a =[ l b =[ l Need Help? 12. [O.19/0.25 Points] DETAILS PREVIOUS ANSWERS SCALCETB 3.1.042. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find in). f(x)=x54X3+xl f'(x)= 5x4712x+1 x Compare the graphs of fand f' and use them to explain why your answer is reasonable. f'(x) = 0 when f has a horizontal tangent 0 J I" is positive when f is increasing 0 J I" is negative when f is decreasing C y 13. [-/0.25 Points] DETAILS SCALCET8 3.1.046. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the first and second derivative of the function. G=fr+6fr G'(r) : G"(r) = Need Help? 14. [-/0.25 Points] DETAILS SCALCET8 3.1.061. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find an equation of the normal line to the tun/e y = that is parallel to the line 2X + y = 1. y: Need Help? 7. [0/025 Points] DETAILS PREVIOUS ANSWERS SCALCETB 3.1.019. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Differentiate the function. 4 3 _ X y~3e + g y: 6x(3)+3ex+k X Check which variable(s) should be in your answer. Need Help? _' 8. [-IO.25 Points] DETAILS SCALCET8 3.1.023.M|. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Differentiate the function. _4x2+2x+4 \"a 1 y: Neee Hem? 9. [IO.25 Points] DETAILS SCALCET8 3.1.032. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Differentiate the function. y:e"+3+6 10. [-/O.25 Points] DETAILS SCALCET8 3.1.034. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find an equation of the tangent line to the curve at the given point. y = 46'" +X, (0, 4) 11. [/0.25 Points] DETAILS SCALCET8 3.1.040.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the equation of the tangent line to the curve at the given point. y=7x76, (1,1) 19. [-/0.25 Points] DETAILS SCALCET8 3.1.078. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the value of c such that the line y = %x + 7 is tangent to the curve y = c. 20. [-/0.25 Points] DETAILS SCALCET8 3.1.503.XP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Differentiate the function. f(X)=X34x+3 r '(x) = Need Help? 21. [-/0.25 Points] DETAILS SCALCET8 3.2.001. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the derivative of f(x) : (1 + 4x2)(x x2) in two ways. Use the Product Rule. rm = Perform the muitiplication rst. rm = 22. [-/0.25 Points] DETAILS SCALCET8 3.2.021. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Differentiate. f ( t ) = Vt t - 9 f' ( t ) = Need Help? Watch It 23. [-/0.25 Points] DETAILS SCALCET8 3.2.027. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find f'(x) and f"(x). f ( x ) = ( x3 + 8 ) ex f' ( x ) = f " ( x) = Need Help? Watch It 24. [-/0.25 Points] DETAILS SCALCET8 3.2.041. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER If f ( x) = x2/(3 + x), find f "(1). f "(1) = Need Help? Watch It