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Derivative of a Constant Function

Power Rule for Positive Integers

The Constant Multiple Rule (POTC)

The Sum + Difference Rule

If f is the function with a constant value c, then df/dx = d'…

If n is an integer and x cannot equal 0,

Pull out the multiplicative constant

Derivative of a Constant Function

If f is the function with a constant value c, then df/dx = d'…

Power Rule for Positive Integers

If n is an integer and x cannot equal 0,

Absolute maximum

Acceleration

Average Rate of Change

Concave Down

The greatest single value that a function attains on a given…

The rate of change of velocity.

For a function f (x) , this represents the total change in f…

A term applied to a section of the graph where the derivative…

Absolute maximum

The greatest single value that a function attains on a given…

Acceleration

The rate of change of velocity.

Intermediate Value Theorem

Mean Value Theorem

Fundamental Theorem of Calculus #1

FTC #2

What Theorem covers this?... If f is continuous on [a,b] and k…

Name this Theorem

What is Theorem called?... The definite integral of a rate of c…

What is this called?

Intermediate Value Theorem

What Theorem covers this?... If f is continuous on [a,b] and k…

Mean Value Theorem

Name this Theorem

Find the zeros of f(x).

Find the intersection of f(x) and g(x).

Show that f(x) is even.

Show that f(x) is odd.

Set the function equal to 0. Factor or use quadratic formula…

Set the two functions equal to each other and solve.... Alternat…

Show that f(-x) = f(x). This shows that the graph of f is sym…

Show that f(-x) = -f(x). This shows that the graph of f is sy…

Find the zeros of f(x).

Set the function equal to 0. Factor or use quadratic formula…

Find the intersection of f(x) and g(x).

Set the two functions equal to each other and solve.... Alternat…

When asked to INTERPRET

Numerical derivative on calculator por…

Rounding

Justification

state when, what, how, and how much

does not require work to be shown

Round to 3 decimals at the end, 5 during work

use what has been given to you

When asked to INTERPRET

state when, what, how, and how much

Numerical derivative on calculator por…

does not require work to be shown

10

5

6

3/2

Evaluate the limit in Part A given the following information:

Evaluate the limit in Part B given the following information:

Evaluate the limit in Part C given the following information:

Evaluate the limit in Part D given the following information:

10

Evaluate the limit in Part A given the following information:

5

Evaluate the limit in Part B given the following information:

Intermediate Value Theorem

Average Rate of Change

Instantenous Rate of Change

Formal definition of derivative

If f(1)=-4 and f(6)=9, then there must be a x-value between 1…

Slope of secant line between two points, use to estimate inst…

Slope of tangent line at a point, value of derivative at a po…

limit as h approaches 0 of [f(a+h)-f(a)]/h

Intermediate Value Theorem

If f(1)=-4 and f(6)=9, then there must be a x-value between 1…

Average Rate of Change

Slope of secant line between two points, use to estimate inst…

Write the notation for the limit of f(…

Write the notation for the limit of f(…

State the 3 conditions of continuity o…

List the 3 situations in which a limit…

1. f(c) is defined... 2. The limit of f(x) as x approaches c exi…

1. Unbounded behavior... 2. Differing left/right behavior... 3. Osc…

Write the notation for the limit of f(…

Write the notation for the limit of f(…

Intermediate Value Theorem

Mean Value Theorem

Rolle's Theorem

Trig Identity: sin2x =

If the function f(x) is continuous on [a,b], and 'y' is a num…

If the function f(x) is continuous on [a,b], AND the first de…

If the function f(x) is continuous on [a,b], AND the first de…

2sin(x)cos(x)

Intermediate Value Theorem

If the function f(x) is continuous on [a,b], and 'y' is a num…

Mean Value Theorem

If the function f(x) is continuous on [a,b], AND the first de…

Average Rate of Change/Average Velocity

Instantaneous Rate of Change/ Instanta…

Horizontal Tangent line

Finding the time when the object hits…

Slope over an interval- use f(x) to make a table

Slope at an instant (Need derivative)

Slope is zero (f prime=0)

Means position is 0 so set s(t)=0 and solve

Average Rate of Change/Average Velocity

Slope over an interval- use f(x) to make a table

Instantaneous Rate of Change/ Instanta…

Slope at an instant (Need derivative)

exponential function

indefinite integral

Absolute minimum

Differentiable

A function of the form f (x) = a x where a is any positive co…

this represents the family of antiderivatives of the function f

The least single value that a function attains on a given int…

A function f is said to be differentiable at a point x = a if…

exponential function

A function of the form f (x) = a x where a is any positive co…

indefinite integral

this represents the family of antiderivatives of the function f

10

5

6

3/2

Evaluate the limit in Part A given the following information:

Evaluate the limit in Part B given the following information:

Evaluate the limit in Part C given the following information:

Evaluate the limit in Part D given the following information:

10

Evaluate the limit in Part A given the following information:

5

Evaluate the limit in Part B given the following information:

Continuity

Limit does not exist (DNE) if

lim as x→0 (sin(x)/x)=

lim as x→[(1-cosx)/x]=

f(c) exists... lim as x→c of f(x) exists... f(c) =lim as x→c of f(x)

Left and right are not qual

1

0

Continuity

f(c) exists... lim as x→c of f(x) exists... f(c) =lim as x→c of f(x)

Limit does not exist (DNE) if

Left and right are not qual

If f'(x)<0 what is true of f(x)?

If f'(x)>0 what is true of f(x)?

Explain how to determine the critical…

If f'(x) is increasing what is true of…

f(x) is decreasing

f(x) is increasing

f'(x)=0 or when f'(x) is undefined

f(x) is concave up

If f'(x)<0 what is true of f(x)?

f(x) is decreasing

If f'(x)>0 what is true of f(x)?

f(x) is increasing

definition of a derivitive

definition of a derivative (alternative)

the derivative does not exist at

difference quotient

Lim h->0 (f(x+h)-f(x)) ÷ (x+h-x)

Lim x->a (f(x)-f(a))÷ (x-a)

corner, cusp, vertical tangent

(f(a+h)-f(a))÷ h

definition of a derivitive

Lim h->0 (f(x+h)-f(x)) ÷ (x+h-x)

definition of a derivative (alternative)

Lim x->a (f(x)-f(a))÷ (x-a)

Intermediate Value Theorem

If f is continuous on [a,b] and k is b…

Rolle's Theorem

If f is continuous on [a,b] and f is d…

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

there is a number c in [a,b] such that f(c)=k.... (Intermediate…

If f is continuous on [a,b] and f is differentiable on (a,b)…

there is at least one number c in (a,b) such that f'(c)=0.... (…

Intermediate Value Theorem

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

If f is continuous on [a,b] and k is b…

there is a number c in [a,b] such that f(c)=k.... (Intermediate…

Critical Point

Inflection Point

Average Rate of Change

Volume by Washers

Possible Critical Point: where f '(x) is 0 OR UNDEFINED ... Indi…

Possible Inflection Point: where f"(x) is 0 OR UNDEFINED... Indi…

Critical Point

Possible Critical Point: where f '(x) is 0 OR UNDEFINED ... Indi…

Inflection Point

Possible Inflection Point: where f"(x) is 0 OR UNDEFINED... Indi…

Find the Zeros

Find the equation of the line tangent…

Find the interval where f(x) is increa…

Find the interval where the slope of f…

f(x)=0

Find a point (x, y) and the slope (using the derivative) then…

f'(x) is positive

f''(x) is positive

Find the Zeros

f(x)=0

Find the equation of the line tangent…

Find a point (x, y) and the slope (using the derivative) then…