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- 1. Multiple Choicef(x)=5
find f'(x)5105x - 2. Multiple Choicef(x)=x3
f'(x)=x23x26x3x - 3. Multiple Choiceg(x)=7x+1
g'(x)=77x7x+10 - 4. Multiple Choicey=5x2+ 3x + 9
dy/dx =10x10x+310x2+310 - 5. Multiple Choicey=9
dy/dx=901undefinded - 6. Multiple Choicey=√x
dy/dx=√x1/√x1/2x-1/2-1/2√x - 7. Multiple ChoiceHere's a tricky one. Consult your pink sheet.
f(x)= 5/x2
df/dx=?10x5/2x5x-2-10x-3 - 8. Multiple ChoiceHere's a tricky one. Consult your pink sheet.
f(x)= 9/∛x
f'(x) =9x-1/3-3x-4/3-9x2/3-3x2/3 - 9. Multiple Choicey=x
dy/dx=x1-10 - 10. Multiple ChoiceWhat does the power rule say for:
axbabxbabxb-1bxa-1Stop the madness - 11. Multiple ChoiceWhat's the product rule:
(fg)'f'g'fg'+g'ffirst times the deriv. of the second + second times the deriv of the firstfirst times the deriv of the second minus second times the deriv of the first - 12. Multiple ChoiceWhat is the quotient rule for (f/g)'?f '/ g'bottom times the deriv of the topbottom times the deriv of the top - top times the deriv of the bottombottom times the deriv of the top - top times the deriv of the bottom over the bottom squared
- 13. Multiple ChoiceFind the derivative of g(x)=(3x-2)/(x2+2)(x2+2)(3)-(3x-2)(2x)
[(x2+2)(3)+(3x-2)(2x)]/(x2+2)2[(x2+2)(3)-(3x-2)(2x)]/(x2+2)2(x2+2)2 - 14. Multiple ChoiceFind the derivative:
f(x) = (-2/3)x3 - (1/2)x2 + 9x-2x2 - x + 9-2x2 + x + 92x2 - x + 92x2 - x - 9 - 15. Multiple ChoiceFind the derivative: y = (x3-1)/(x3)3x/x6[x3(3x2-1)-(x3-1)(3x2)]/(x3)2[x3(3x2)-(x3-1)(3x2)]/(x3)2(3x - 1)/x3
- 16. Multiple ChoiceDerivative means the same thing asslope of the tangent lineslope of the normal lineexponentpotato
- 17. Multiple ChoiceWhat is the derivative of sin(x)?sin(x)cos(x)-sin(x)-cos(x)
- 18. Multiple ChoiceWhich if the following is not a correct notation for 'derivative?'f'(x)y'dydy/dx
- 19. Multiple ChoiceFind the slope of the tangent line to f(x) = -3x2-6x at x = 1.m = 0f'(x) = -6x - 6f'(x) = 6xm = -12
- 20. Multiple ChoiceFind the second derivative of the function:
f (x) = 2x - 5x6f ''(x)= 2 - 30xf ''(x) = 2-30x5f ''(x) = -30x5f ''(x) = -150x4 - 21. Multiple ChoiceFind the derivative: h(x)=(3x+2)(5x3+2x)(3x+2)(15x2+2x)+(5x3+2x)(3)(3x+2)(15x2+2)(5x3+2x)(3)(3x+2)(15x2+2)+(5x3+2x)(3)60x3+30x2+12x+4
- 22. Multiple ChoiceFind the derivative: j(x)=(5x-2)(2-4x)(5x-2)(2-4x)-(2-4x)(5)(5x-2)(4)+(2-4x)(5)(5x-2)(-4)+(2-4x)(5)(5x-2)(-4x)-(2-4x)(5)
- 23. Multiple ChoiceIf a function has a derivative that is negative, what does that tell you?The function is increasingThe function is decreasingwho knowsplease stop...I can't take it anymore
- 24. Multiple ChoiceFind the second derivative of the given function
f(x) = x4 + 4x3 - 2x212x2 + 24x - 44x3 + 12x2 - 4x4x + 12x - 4x4x3 + 12x2 - 4x - 25. Multiple ChoiceDifferentiate f(x) = 5x7.35x6210x55x61050x4
- 26. Multiple Choice
Where is the graph not differentiable?x = -2, -1, 0, 1x = -2, -1, 1x = -2, -1x = -1, - 27. Multiple ChoiceWhere is the graph neither continuous nor differentiable?x = -1, 0, 1, 2x = -1, 1x = -1, 0, 1x = -1, 0, 2
- 28. Multiple ChoiceWhat is the derivative of xn?(n-1)xnnxn+1(n+1)xn-1nxn-1
- 29. Multiple ChoiceSolve f '(2) for
f(x) = x2 + 2x2x + 26122x - 30. Multiple ChoiceWhich is the derivative of this function?ABCD
- 31. Multiple ChoiceFind the derivative of f(x) = 6x30 -2x15 + 4x3 - 2x + 1f'(x) = 18x29 + 30x15 + 12x3f'(x) = 180x29 - 30x14 + 12x2f'(x) = 180x29 - 30x14 + 12x2 - 2f'(x) = 180x29 - 30x14 + 12x2 +1
- 32. Multiple ChoiceHow many derivatives can you take of a function?only 3only 2only 1until you can no longer derive it
- 33. Multiple ChoiceWhen we "take the derivative" of a function what are we finding?What's a derivative?The rate at which our struggles in Calculus are increasing.The slope of the secant lineThe slope of the tangent line
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