Basic 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?
Find the derivative of
(2x^3 +1)(x-2)
What is
8x^3 -12x^2 +1
The Profit Function given is
P=-(1/15)x^3+4000x^2-120x-144000
What is the Marginal Profit Function?
Find the derivative of
3x^2+2x-1
What is
State the formula of the Product Rule for Derivatives
What is
f*g' + g * f'
A line that touches a curve at a specific point and reveals the slope of the curve at that specific point. Name this type of line.
What is a Tangent Line?
Find the derivative of
sqrtx(3x-1)
What is
(9x-1)/(2sqrtx)
3sqrtx+(3x-1)/(2sqrtx
Revenue = (_____ * ______)
Profit = (______ - _______)
What is R = xp and P = R - C
What is the derivative of
2/(x-1)
What is
-2/(x-1)^2
State the Quotient Rule
What is
(g*f'-f*g')/g^2
Find this equation's derivative: 4x^3 + 7x^2 + 2x + 3
What is 12x^2 + 14x + 2
Find the derivative of
(4x-5)/(2x+3)
What is
22/(2x+3)^2
Find the average velocity over the time interval [1, 1.6]
s(t)=-16t^2-16t+320
What is -57.6 ft/s
Find the derivative of
sqrt(3x-5)
What is
3/(2sqrt(3x-5)
A function fails to be differentiable if it has a....
What is a discontinuity, node, cusp or a vertical tangent
1/x + sqrtx/x
What is the derivative of
-1/x^2 -1/(2sqrtx^3)
Find the derivative
((2x-1)/(5x-3))^3
What is
-3(2x-1)^2/(5x-3)^4
If the position function of an object is given below, with what speed will the object hit the ground?
s(t)=-16t^2-16t+320
144 ft/sec
Find the derivative of
x^3-2x
What is
3x^2-2
The Father of Calculus
What is Isaac Newton
The following is the derivative of what?
12x^2-10x+4
What is
4x^3 -5x^2+4x-1
Find the derivative of
2tsqrt(t+6)
What is
3(t+4)/(t+6)^(1/2)
Find the Marginal Profit for 700 units given the following demand and cost functions.
p=1700-0.016x
C=715000+240x
What is $1437.60
Find the derivative of
x^5
What is
5x^4
The zeros of a derivative show where what takes place
A maximum or minimum