What is the limit of six /x as x approaches 0?
1
Options for evaluating limits.
1) Factor
2) Substitute
3) Conjugate
When to use L'Hopital
0/0 or infinity/ infinity
Derivative of tan x
Derivative of cot x
Derivative of sec x
Derivative of csc x
Derivative of inverse sin x
Derivative of inverse cos x
Derivative of inverse tan x
Derivative of inverse cot x
If functions f and g are inverses and the point (a, b) is on the graph of f, then what is g'(b)?
1/ f'(a) or 1/ f'(g(x))
Tangent Line formula
f'(a)(x-a) +f(a)
MVT
f'(c) = f(b) - f(a) / b - a
slope of tangent line is equal to secant line
derivative at x = c is the same as the average rate of change of the interval
How to find if a graph is increasing or decreasing
f'(x) > 0, f(x) is increasing
f'(x) < 0, f(x) is decreasing
How to find if a graph is concave up or down
f"(x) > 0 then f(x) is concave up
f"(x) < 0 then f(x) is concave down.
How to find the point of inflection
f"(x) changes from positive to negative or negative to positive
What is speed?
The absolute value of velocity
Reimann sum
Antiderivative of 1/x
ln |x| + c
Average value of a function
Net Change of a function
Integral from a to b of f'(x) = f(b) -f(a)