Calculus Index Cards Front And Back

Instructions The odd numbered slides are the front of the index card, the questions The even numbered slides are the back, the answers Write the front of the card and then write the back and carry the stack with you at all times

Given Velocity and Position at t = 0 Find speed Acceleration Position Function Distance traveled Front

Back

Given position find average velocity from a to b Given a table of amounts, find the rate of change at one of those amounts Given a function from a, to b, find the average value Given velocity from a to b, find the average velocity Front

old fashion slope from a to b Given position find average velocity from a to b old fashion slope from a to b Given a table of amounts, find the rate of change at one of those amounts Old fashion slope around that point Given a function from a, to b, find the average value Given velocity from a to b, find the average velocity

Given A. Use the left hand rule B. Use the right hand rule C. Use the midpoint rule D. Use the trapezoid rule

Given A. Use the left hand rule B. Use the right hand rule C. Use the midpoint rule D. Use the trapezoid rule

Find the equation of the line tangent to the curve Find the equation of the line normal

Given And the graph of f(x) Find g(some number) Find g’(x), find g’(some number) Find where g has a max/min Find the point of inflection of g

Given And the graph of f(x) Find g(some number) Find g’(x), find g’(some number) Find where g has a max/min Find the point of inflection of g

Function is continuous if (informal definition) (Formal definition) Function is differentiable if (informal) (formal)

Function is continuous if (informal definition) (Formal definition) Function is differentiable if (informal) (formal)

Mean Value theorem Extreme Value Theorem

The derivative of this Is this

The derivative of this Is this

The derivative of is

The derivative of is

The derivative of is

The derivative of is

The first derivative tells us about

The first derivative tells us about Slope Instantaneous rate of change Increasing or decreasing Max, min

The second derivative tells us

The second derivative tells us Concave up concave down Point of inflection Rate of change of the slopes The maximum/minimum slope

Product rule Quotient rule Chain rule

Product rule Quotient rule Chain rule

The antiderivative of is

The antiderivative of is

The antiderivative of is

The antiderivative of is

What is this? or

What is this? or Definition of the derivative

Find the answer

Find the answer

First derivative test f’<0 when x<a and f’>0 when x>a. What does that mean at x = a f’>0 when x<a and f’<0 when x>a. What does that mean at x = a

First derivative test a is a min a is a max f’<0 when x<a and f’>0 when x>a. What does that mean for x = a a is a min f’>0 when x<a and f’<0 when x>a. What does that mean for x = a a is a max

Second derivative Test f ’(a) = 0 and f ”(a)<0. What does that mean at f(a)? f ’(a) = 0 and f ”(a)>0. What does that mean at f(a)?

Second derivative Test f ’(a) = 0 and f ”(a)<0. What does that mean at f(a)? f(a) is a max f ’(a) = 0 and f ”(a)>0. What does that mean at f(a)? f(a) is a min

What is the general solution for the following

What is the general solution for the following

Find the derivative of the following

Find the derivative of the following

underestimate or overestimate? left hand rule with a function that is increasing right hand rule with a function that is increasing tangent line approximation with a curve that is concave down tangent line approximation with a curve that is concave up

underestimate or overestimate? left hand rule with a function that is increasing - under right hand rule with a function that is increasing - over tangent line approximation with a curve that is concave down - over tangent line approximation with a curve that is concave up - under

is speed increasing or decreasing velocity is positive and acceleration is negative velocity is negative and acceleration is negative

is speed increasing or decreasing velocity is positive and acceleration is negative - decreasing velocity is negative and acceleration is negative - increasing

Critical points are

Critical points are when the derivative = 0 or is undefined at the endpoints of a closed interval