Derivatives
The derivative of sin(x)
cos(x)
∫1/x
ln(x)
This theorem guarantees a point where f'(c) = average rate of change
Mean Value Theorem
A graph is concave up when this is true
What do you call an integral that's late
An improper integral
d/dx [x^3 + 2x]
3x^2+2
∫3x^2
x^3
This theorem connects integration and differentiation
FTC
This happens where the second derivative is 0 and changes sign
Inflection value OR the graph changes concavity
Why did the function break up with is derivative
There was a discontinuity
d/dx[(3x^2+2x)^4]
4(3x^2+2x)^3 * (6x+2)
∫e^(2x)
1/2e^(2x)
This part of this theorem is used to find the value of f(c) given f(0) and f'(x)
FTC Part II
This function has vertical asymptotes at x = π/2 and at x = -π/2
arctan(x)
What do you call a derivative that went rogue
derivrogue
Implicit differentiation of xy=5
xdy/dx+y=0
∫sec^2(x)dx
tan(x) + C
Rolle's Theorem requires these 3 conditions
Dont do this one
NANANAN
Why was the integral at therapy
it was derived