Derivatives
The slope of a line that lies tangent to the curve at a given point
What is a derivative?
The process of finding the derivative of a dependent variable in an implicit function by differentiating each term separately.
What is implicit differentiation?
To find the anti-derivative of an equation is to...
What is to find the integral?
The two numbers whose sum is 24 and whose product is a maximum.
What is x=12 y=12
State the product rule.
What is a'b + b'a?
Find this derivative of the following equation: f (x) = x5-3x4
What is 5x4 - 12x3 ?
A function fails to be differentiable if it has...
What is discontinuity, a sharp corner/edge, or a vertical tangent?
Integrate the equation: 5/1-e3x
What is -5/3(ln le-3x - 1l + C
Each side of x of a square is increasing at a constant rate of 3in/sec. How fast is the area decreasing when x = 5?
What is dA/dt = 30 in2/sec?
Find the equation of the tangent line of f(x) = sin x at the given point x=7pi/6
What is y - 1/2 = √3/2 (x - 3pi/4)?
The definition of a derivative.
What is the equation : lim x-->0 (f (x+h) - f (x)) / h ?
Use implicit differentiation to find the derivative: 3y2
What is 6yy' ?
Find f(x) if f'(x) = 12x2(x3 + 1)3 and f(1) = 19.
What is f(x) = (x3 + 1)4 + 3?
An open box with a rectangular base is t be constructed from a 12'' by 18'' piece of cardboard by cutting out squares from each corner and bending up the sides. Find the dimensions of the box that will have the largest volume.
What are the dimensions 7.2in x 2.4in x 13.2in
Estimate the area under the graph f(x) = 2x + 2 using a left hand Reimann sum.
What is 28 units2
Name three derivative rules.
What are the product, quotient, and chain rules?
Find the slope of the graph x2 - 9y2 = 16 at the point (5, 1)
What is y' = (x-3) / 9y
Integrate the equation: x(7-6x2)5
What is -1/72[(7-6x2)5] + C?
Water leaking on a floor creates a circular pattern on the grounf at the constant rate of 12ft3/min forms a conical pile whose altitude is 2/3 of the radius of the base. How fast is the height of the pile increasing when the base radius is 6ft?
What is dh/dt = 1ft/2min
Find the derivative of f(x) = -2xe3x
What is f'(x) = -2e3x(1 + 3x)
Find all the points on the graph of f(x) = sin x where the slope of the tangent = 1/2
What is 5pi/3 + 2pik
Find y' implicitly for the following equation: xy2 - e5x + 3y3 = 3
What is y' = (5e5x - y2 ) / 2yx + 9y2
Find the definite integral of -3√x from 1 to 4.
What is -14?
A farmer has 120ft of fencing and wants to construct 3 pig pens by building a fence around a rectangular region, then subdividing the region into 3 smaller rectangles by placing 2 fences parallel to one side of the rectangle. What dimensions of the region maximizes the total area?
What are the dimensions 30ft x 15ft?
For the graph y = x, find the domain that would underestimate the area using a right hand Reimann sum.
What is (-infinity, 0)