f'(x) + g'(x)

cf'(x)

f(x)g'(x) + g(x)f'(x)

f'(x) - g'(x)

derivative of the summation of two functions

derivative of a constant times a function

derivative of the multiplaction of two functions

derivative of the difference between two functions

f'(x) + g'(x)

derivative of the summation of two functions

cf'(x)

derivative of a constant times a function

1.) F(c) exists... 2.) limit F(x) as x app…

Yes lim+=lim-=f(c)... No, f'(c) doesn't ex…

This is a graph of f'(x). Since f'(C) e…

1

f is continuous at x=c if...

Given f(x):... Is f continuous @ C... Is f' continuous @ C

Given f'(x):... Is f continuous @ c?... Is there an inflection point…

1.) F(c) exists... 2.) limit F(x) as x app…

f is continuous at x=c if...

Yes lim+=lim-=f(c)... No, f'(c) doesn't ex…

Given f(x):... Is f continuous @ C... Is f' continuous @ C

f is continuous at x=c if...

Intermediate Value Theorem

Global Definition of a Derivative

Alternative Definition of a Derivative

If f is continuous on [a,b] and k is a number between f(a) and…

f '(x) is the limit of the following difference quotient as x…

f is continuous at x=c if...

Intermediate Value Theorem

If f is continuous on [a,b] and k is a number between f(a) and…

1.) F(c) exists... 2.) limit F(x) as x app…

Yes lim+=lim-=f(c)... No, f'(c) doesn't ex…

This is a graph of f'(x). Since f'(C) e…

1

f is continuous at x=c if...

Given f(x):... Is f continuous @ C... Is f' continuous @ C

Given f'(x):... Is f continuous @ c?... Is there an inflection point…

1.) F(c) exists... 2.) limit F(x) as x app…

f is continuous at x=c if...

Yes lim+=lim-=f(c)... No, f'(c) doesn't ex…

Given f(x):... Is f continuous @ C... Is f' continuous @ C

Derivative of a Constant Function

Power Rule

Derivative Constant Multiple Rule

Derivative of a Sum or Different

df/dx (c)= 0... If f has the constant value f(x)= c, then it equa…

d/dx x^n = nx^n-1... If n is any real number, then the above hold…

d/dx (cu)= c du/dx... If u is a differentiable function of x, and…

d/dx (u+v)= du/dx + dv/dx... If u and v are differentiable functi…

Derivative of a Constant Function

df/dx (c)= 0... If f has the constant value f(x)= c, then it equa…

Power Rule

d/dx x^n = nx^n-1... If n is any real number, then the above hold…

definition of a limit

f(x)=IxI

Squeeze Theorem

Definition of Continuity at a point

if and only if L is the one number we can keep f(x) arbitraril…

IxI= {x if x is greater than or equal to 0}... {-x if x less tha…

If lim f(x) = lim g(x) = L than f(x) ≤ h(x) ≤ g(x)... x→a x→a... f…

f(x) is continuous at x=a if and only if f(a) and ... lim f(x) bo…

definition of a limit

if and only if L is the one number we can keep f(x) arbitraril…

f(x)=IxI

IxI= {x if x is greater than or equal to 0}... {-x if x less tha…

Fundamental Theorem of Calculus (part 2…

Integral of dx/(sqrt(1-(x^2))) =

Integral from a to b of (rate of change…

Fundamental Theorem of Calculus (part 1…

F(b) - F(a), where F is an antiderivative of f.

arcsin(x) + C

The amount which that quantity has changed from t = a to t = b.

f(x)

Fundamental Theorem of Calculus (part 2…

F(b) - F(a), where F is an antiderivative of f.

Integral of dx/(sqrt(1-(x^2))) =

arcsin(x) + C

Rate

Derivative

Infinitesimal

Speed

The amount that one quantity changes with respect to another.

Infinitesimal change in the y value due to an infinitesimal ch…

Extremely small

The change in position over time

Rate

The amount that one quantity changes with respect to another.

Derivative

Infinitesimal change in the y value due to an infinitesimal ch…

1.) F(c) exists... 2.) limit F(x) as x app…

Yes lim+=lim-=f(c)... No, f'(c) doesn't ex…

This is a graph of f'(x). Since f'(C) e…

1

f is continuous at x=c if...

Given f(x):... Is f continuous @ C... Is f' continuous @ C

Given f'(x):... Is f continuous @ c?... Is there an inflection point…

1.) F(c) exists... 2.) limit F(x) as x app…

f is continuous at x=c if...

Yes lim+=lim-=f(c)... No, f'(c) doesn't ex…

Given f(x):... Is f continuous @ C... Is f' continuous @ C

Changing direction (left/right/up/down)

Displacement from t1 to t2

Velocity

Average velocity

Velocity=0 AND changed sign

Change in position... s(t2) - s(t1)

rate of change of position

Slope of position s(t2)-s(t1)/t2-t1

Changing direction (left/right/up/down)

Velocity=0 AND changed sign

Displacement from t1 to t2

Change in position... s(t2) - s(t1)

1.) F(c) exists... 2.) limit F(x) as x app…

Yes lim+=lim-=f(c)... No, f'(c) doesn't ex…

This is a graph of f'(x). Since f'(C) e…

1

f is continuous at x=c if...

Given f(x):... Is f continuous @ C... Is f' continuous @ C

Given f'(x):... Is f continuous @ c?... Is there an inflection point…

1.) F(c) exists... 2.) limit F(x) as x app…

f is continuous at x=c if...

Yes lim+=lim-=f(c)... No, f'(c) doesn't ex…

Given f(x):... Is f continuous @ C... Is f' continuous @ C

acceleration due to gravity

solving equations with unknown exponents

Concavity Test

point of inflection

9.8 m/s^2 or 32 feet/sec^2 - the second derivative

2ish methods - ... #1 - get common basis... "Solve 2x = 32" ... conv…

The graph of a twice-differentiable function y=f(x) is... (a) con…

the point where the graph changes concavity - find by identify…

acceleration due to gravity

9.8 m/s^2 or 32 feet/sec^2 - the second derivative

solving equations with unknown exponents

2ish methods - ... #1 - get common basis... "Solve 2x = 32" ... conv…

1.) F(c) exists... 2.) limit F(x) as x app…

Yes lim+=lim-=f(c)... No, f'(c) doesn't ex…

This is a graph of f'(x). Since f'(C) e…

1

f is continuous at x=c if...

Given f(x):... Is f continuous @ C... Is f' continuous @ C

Given f'(x):... Is f continuous @ c?... Is there an inflection point…

1.) F(c) exists... 2.) limit F(x) as x app…

f is continuous at x=c if...

Yes lim+=lim-=f(c)... No, f'(c) doesn't ex…

Given f(x):... Is f continuous @ C... Is f' continuous @ C

f is continuous at x=c if...

Intermediate Value Theorem

Global Definition of a Derivative

Alternative Definition of a Derivative

If f is continuous on [a,b] and k is a number between f(a) and…

f '(x) is the limit of the following difference quotient as x…

f is continuous at x=c if...

Intermediate Value Theorem

If f is continuous on [a,b] and k is a number between f(a) and…

f'(x) + g'(x)

cf'(x)

f(x)g'(x) + g(x)f'(x)

f'(x) - g'(x)

derivative of the summation of two functions

derivative of a constant times a function

derivative of the multiplaction of two functions

derivative of the difference between two functions

f'(x) + g'(x)

derivative of the summation of two functions

cf'(x)

derivative of a constant times a function