Derivatives
A function that models the slope of the curve for all x-values for which it exists. This is the definition of what?
What is the definition of a derivative?
A left side rectangle
What is a rectangle that intersects a function on the top left
The area formula for a trapezoid
What is 1/2 height x (sum of the 2 bases)
Name 3 of the rules to find limits
What is Difference Rule, Constant Multiple Rule, Product Rule, Power Rule, Quotient Rule
State the formula of the Power Rule for Derivatives
What is A'b + B'a
A line that passes through the curve at x=a and has a slope m=f '(a). Name this type of line.
What is a Tangent Line?
Evaluate the following. ∫(sin x+2)dx
What is -cos x + 2x + C ?
The meaning of capital sigma
What is repeated addition?
State the definiton of a global limit.
What is limits involving infinity
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: 4x3 + 7x2 + 2x + 3
What is the 12x2+14x+2
The fundamental theorem of Calculus
What is the integral of f'(x) from a to b with respect to x = f(b) - f(a)
When a function would produce negative area
What is under the x-axis
Answer the following Limit Question: Lim x^2-3x-10/x^2-25 x->2
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
The Product Rule
What is f'g+g'f
What is the ex + C?
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?
Answer the following Global Limit Equation 7x^4+2x^7/4x^7
What is 1/2
Integrate the following equation ∫√(7x+9)dx
(2/21)(7x+9)^(3/2)+C
Name 5 derivative shortcuts
Answer will vary...
The two part chain rule
What is outside'(inside) X inside'
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 the 4 types of Discountinuties
What is Hole, Jump, Infinity, Oscillating
Find dy/dx and d^2y/dx^2 of the following equation y=3x^4-4x^(3/2)
What is 12x^3-6x^(1/2) and 48x^2-3x^(-1/2)