When I see the words
"Find the relative extrema"
What is "set the derivative = 0"
The derivative of 5x-2
What is -10x-3
This theorem says basically that the slope of a tangent line equals the average rate of change
What is the Mean Value Theorem
intx^7dx
What is
1/8x^8+C
The method needed to integrate
(4x^2+6x-1)*(8x+6)
What is u-substitution
"Find the average value"
What is integral over interval
The derivative of sin(6x)
What is 6*cos(6x)
This theorem says that a continuous function on a close interval must have absolute extrema
What is the Extreme Value Theorem
int1/x^5dx
-1/(4x^4)+C
This results when a region revolves around an axis that is fully touches (no gaps).
What is a volume (of a disk)
"The derivative of f(x)/g(x)"
What is quotient rule
The derivative of tan-1(x)
What is
1/(1+x^2)
This is where you find critical points
What are points where the derivative = 0 or is undefined
int1/xdx
What is ln|x|
This results when a region is revolved around an axis but has a gap between the region and the axis.
What is a volume (by washers)
"Solve dy/dx = 3xy2"
What is separation of variables
The derivative of
1/x^6
What is
-6/x^7
This is the consequence of a positive second derivative at a critical point.
What is a relative minimum.
inte^(6x)dx
What is
1/6e^(6x)+C
To solve the below by hand:
int_2^8f(x)dx
What is the Fundamental Theorem of Calculus (FTC)
"The derivative of f(g(x))"
What is the Chain Rule
The derivative of
e^(10x)
What is
10e^(10x)
(d^5y)/(dx^5)
What is the fifth derivative
intsin(9x)dx
What is
-1/9cos(9x)+C
The result of
d/dx(int_0^xf(t)dt)
What is
f(x)