1/(b-a) times the antiderivative from a to b of f(x)dx
200
What is the derivative of x with respect to x?
1
200
What is the antiderivative (du/u)?
ln |u|+c
200
Justify g is increasing from a to b
g'(x) is greater than zero for all x from a to b
200
What is total distance?
The antiderivative from a to b of the absolute value of velocity
200
What is the limit as x approaches 0 of (sin x)/x?
1
300
What is derivative of ln u?
du / u
300
What is the antiderivative of (sec u)(tan u)du?
sec u+c
300
Justify h(c) is a relative minimum of h
h'(x) changes sign from negative to positive at c
300
When is a function continuous?
f(c) is defined, the limit as x approaches c of f(x) exists, and the limit as x approaches c of f(x) equals f(c)
300
In the second derivative test for extrema, what must you do if f"(c)=0?
The test fails, use the first derivative test for extrema
400
What is the derivative of csc u?
-(csc u cot u)du
400
What is the antiderivative of (a^u)du?
(1/ln a)(a^u)+c
400
When is there a point of inflection of f at c?
When f"(x) changes sign at x=c
400
When is speed increasing?
When velocity and acceleration have the same sign
400
What is the cross sectional area equation for a semicircle?
A=(pi/8)(b^2)
500
What is the derivative of arc cot u?
-(du)/(1+u^2)
500
What is the antiderivative of (csc u)du?
-ln|csc u+cot u|+c
500
Justify g(c) is a relative maximum using the second derivative test for extrema
g"(c) is less than zero and g' must equal zero at c
500
What acronym is helpful to complete a related rates problem?
GFEDS
500
What is Rolle's Theorem?
If a function is continuous on a closed interval, differentiable on an open interval and the y values of a and b are equal, there is a horizontal tangent line at c, or f'(c)=0