Show:
Limits (algebraically)
Derivatives
(long way)
Derivative Tricks
Implicit Derivatives
First and Second Derivative Tests
100
limit as x->2 (x^2-3x+2)/(x-2)
What is 1.
100
Find the derivative of f(x)=x^2
What is 2x.
100
Derivative of f(x)=3x^5+2x^3+4x+7
What is f'(x)=15x^4+6x^2+4.
100
Find the derivative with respect to x for 3y^3+x^2=5.
What is dy/dx = -2x/(9y^2).
100
Find the critical points of f(x)=2x^3-6x^2+2.
What is (0,2) and (2,-6).
200
limit as h->0 sin(9h)/h
What is 9.
200
The derivative of f(x)=1/x
What is -1/(x^2).
200
Derivative of f(x)=secx.
What is f'(x)=secxtanx.
200
Find the derivative with respect to x for 4x^2y+10xy=200y.
What is dy/dx=(-10y-8xy)/(4x^2+10x-200).
200
Use the First Derivative Test to find the relative min and relative max for f(x)=x^3-27x-20.
What is relative max at (-3,34) and relative min at (3,-74).
300
limit as t->0 (1-cost)/sint
What is 0.
300
Find the derivative of f(x)=2x^2+10x and use it to find the slope of the tangent line at a=3.
What is 22.
300
Find the derivative of f(x)=(2x^4-4x^(-1))*(secx).
What is f'(x)=(2x^4-4x^(-1))*(secxtanx)+secx(8x^3+4x^(-2)).
300
Find the derivative with respect to x for xsiny-ycosx=2
What is dy/dx=(-siny-ysinx)/(xcosy-cosx)
300
Use the first derivative test to find the relative max and min of f(x)=3x^4+8x^3-6x^2-24x.
What is relative mins at (-2,8) and (1,-19) and relative max at (-1,13).
400
limit as t->0 (4^(2t)-1)/(4^t-1)
What is 2.
400
Find the derivative of f(x)=sqrt(x) and use it to find the slope of the tangent line at a=4.
What is 1/4.
400
Find the derivative of f(x)=(1+tanx)/(1-tanx).
What is f'(x)=(2(secx)^2)/(1-tanx)^2
400
Find the equation of the tangent line of x^2+y^2=8 at (2,-2).
What is y+2=x-2.
400
Find the horizontal and vertical asymptotes of f(x)=(4x^2-10)/(x^2-4).
What is x=2 and x=-2 and y=4.
500
limit as x->infinity 3x^3+4x^2-10/(x^2-6x+8)
What is infinity (or undefined).
500
Using the derivative of f(x)=sqrt(x), find the equation of the tangent line at (9,3)
What is (y-3)=1/6(x-9).
500
Find the slope of the tangent line of f(x)=(x^4-4)/(x^2-5) at x=2.
What is -80.
500
Find the equation of the tangent line of (x+2)^2-6(2y+3)^2=3 at (1,-1).
What is 1/4.
500
Use the second derivative test to find the critical points, inflection points, concavity, and the graph of the function: f(x)=x^4-4x^3+10.
What is critical points: (0,10) and (3,-17), inflection points: (0,10) and (2,-6), concave up at x=3.