AB Calc Review

Inverse

100

If point (a,b) lies on the inverse function f^-1, then what point lies on function f?

(b,a)

200

To find the equation of the inverse of a function...

Interchange X and Y, then solve the equation for Y

300

To graph the inverse of a function...

Reflect the graph of the function across the line y=x

400

Inverse of y=lnx

y=e^x

500

Inverse of y=e^x

Y=ln(x)

Derivative

100

f'(a)=0 and f''(a)<0, f...

f has a maximum at x=a

200

Slope of the line tangent to f at x=a

f'(a)

300

Increasing speed...

Velocity and acceleration have the same sign

400

Mean Value Theorem If f is continuous on [a,b] and differentiable on (a,b), then...

for some c in (a,b), f'(c)=(f(b)-f(a))/(b-a)

500

d/dx (f+g)= 

f'+g'

Integral

100

∫e^udu

e^u+c

200

Separable differential equation

∫ f(y)dy = ∫g(x)dx

300

∫du/u

ln|u|+c

400

Volume (by washers)

ΔV = 𝝿(R²-r²)Δx

500

General Solution of dx/dt = kx

x=ce^kt

Pre-Calculus

100

ln|1|=

0

200

Area of a triangle 

A= 1/2bh

300

Pythagorean Theorem

a²+b²=c²

400

e^lnx=

x

500

Rewrite log(AB)

log(A)+log(B)