Derivatives
A function that models the slope of the curve for all x-values for which it exists. This is called what?
What is the definition of a derivative?
State the Definite Integral formula.
What is ∫_a^b f(x)dx
The formula for finding the area between 2 curves.
What is the integral from a to b of f(x)-g(x) dx?
Name 3 methods to find limits.
What is substitution, graphically, factor/cancel...
answers may vary
State the formula of the Product Rule for Derivatives
What is a'b + b'a
A line that passes through the curve at x=a and has a slope m=-1/F '(a). Name this type of line.
What is a Normal Line?
Evaluate the following. 0 to pi ∫ (sin x+2)dx
What is 2pi + 2?
In the disk method cross sections are this shape.
What is a circle or disk?
State the 3 rules for infinity limits.
bottom heavy -> 0
top heavy -> infinity
equal degrees -> take the ratio of the coefficients
Find any points where the graph fails to be differentiable and explain why 3√(5x+7)
What is y is not differentiable at x=-7/5 due to a vertical tangent
Find this equation's derivative: 4x^3 + 7x^2 + 2x + 3
What is the derivative of 12x^2 + 14x + 2
State 3 Definite Integral Rules.
What is constant rule, constant multiple, sum and difference and backwards/rule power rule.
This formula is used to find areas with more than one curve.
What is ∫_a^b(f(x)-g(x) )dx?
Answer the following Limit Question: Lim x->2 (x^2-3x-10/x^2-25)
What is L=4/7
A function fails to be differentiable if it has a....
What is a discontinuity, corner, cusp or a vertical tangent
What is the long definition of the derivative?
Lim h->0 f(x+h)-f(x)/h
This equation's derivative is: 25x^3 - 12x^2 + X. Find its intergral...
What is the derivative of 25x^4/4 - 4x^3 + x^2/2?
All cross sections to find a volume will be in circle form, the formula for the cross section is A(x)= A= pi r^2. Name this method..
What is the Disk Method?
The limit as x->infinity (7x^4+2x^7)/(4x^7)
What is 1/2
Integrate the following equation ∫(7x+9)dx
3.5x^2+9x+C
Name 3 Derivative rules
Answer will vary...
Integrate -1 to 3 ∫((2x+1)^2)dx.
What is 57 1/3?
Find the area enclosed by y=x^2 and the y-axis between [0,3] is revolved around the y-axis.
What is 9/2 pi
Name 3 types of Discountinuties
What is Hole, Jump, Infinity, Oscillating
Find dy/dx and d^2y/dx^2 (second derivative) of the following equation y=3x^4-4x^(3/2)
What is 12x^3-6x^(1/2) and 48x^2-3x^(-1/2)