Derivatives
Integrals
Methods
Solving Derivatives
Pot Luck
100
How do you find the critical numbers of a function?
Set first derivatives equal to zero.
100
Evaluate: sin(3x)dx
1/3 cos(3x) +C
100
What does the derivative measure?
The slope of a function
100
(Using your whiteboard) What is the first derivate of f(x)= 4x^3 + 8x^2 + 5x + 7
12x ^2 + 16x + 5
100
Write the first four nonzero terms for the Maclaurin series for cos(x)
What is cosx = 1 - x^2/2! + x^4/ 4! -x^6/6!
200
Which derivative do you use to find the points of inflection?
What is the second derivative?
200
Solve the integral of (5x^2+4x-2)dx, from 3 to 6
What is 363?
200
What rule is: f'(x)g(x)+ f(x)g'(x)
What is the product rule?
200
lim x->0 e^x-1/ 2x (Hint: Don't HURT yourself on this one and have to go to a HOSPITAL)
What is 1/2?
200
lim 3x^4 + 5x ^3 +8 / 5x^2 + 9x^4
1/3
300
When talking about particles which derivative is used to find a particle's acceleration?
What is the second derivative?
300
If f'(x) = 12x^2 - 6x + 1, f(1)=5, then f(0) equal what?
What is 3?
300
What is this rule used for: f'(c)= f(b) - f(a) / b-a
What is the Mean Value Theorem
300
What is the derivative of y=ln^3x
What is 3ln^2 x (1/x)?
300
Find the Maclaurin Polynomial of degree n f(x) = e^-x, n=3
What is 1-x + x^2/2! -x^3/3!
400
What is the second derivate test?
What is plugging the critical numbers into the second derivative to find relative max and min?
400
Evaluate the indefinite integral: xe^-x dx
What is -xe^-x - e^-x + C
400
What are the three rules of Rolles Theorem
What is 1. Continuous on [a, b] 2. Diff on (a, b) 3. f(a) = f(b)
400
Find the derivative: y= x^2 tan1/x
What is dy/dx = 2x tan (1/x) - sec^2 (1/x)
400
Evaluate the indefinite Integral (2x^2 - 1)^2 dx
What is 4/5x^5 - 4/3x^3 -x + C
500
What is the general derivative of a^x
What is ln(a) a^x?
500
If the integral x^2 cosx dx = h(x) - integral 2x sinx dx, then h(x) = (Hint: This equation looks like there are too many PARTS)
What is x^2 sinx + C
500
Which is used when the center is 0, Taylor or Maclaurin?
What is the Maclaurin Series?
500
What is the maximum value of the function with the first derivative such as: f'(x) = e^x - 3x^2
What is x = .91?
500
Find dy/dx for x^2 + y^2 = 36
What is -x/y
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