phrases to know for calc test

average rate of change

f(b) - f(a) / b - a

instantaneous rate of change

lim h → 0 f(x+h) - f(x) / h

normal line

m = -1/f’(a)

horizontal tangent means slope is

zero

velocity

v(t) = s’(t)

speed

absolute value of velocity

acceleration

a(t) = v’(t) = s’’(t)

estimate derivative

use average rate of change

way to format frq

at time t = ___ , the (put context here) is changing at a rate of (#) (units)

how to know if differentiable in piecewise function

is continuous and left-hand slope and right-hand slope are equal to one another

parallel lines

1. find slope

2. calculate derivative

3. set f’(x) = m and solve for x

4. plug the x value into original equation to get y coordinate

5. pt slope form ( y - y1 = m (x - x1)

write equation of the line tangent to the graph ___ at the point x = __

1. find “y” by plugging given “x” into equation

2. find slope by derivative, then plug in “x” to get slope

3. write answer in pt slope form

find values of a and b in piecewise function that make f(x) differentiable

1. plug in value to both piecewise functions and set them equal

2. take derivative of both

3. solve for one variable, then find the other variable

when looking at a graph and asked for f’(a)

rise over run at that point

intervals where f’(x) > 0 on graph in other words

where is the original graph f(x) going UP from left to right

At what value(s) of x is f not differentiable on a graph

• discontinuities

• sharp corners

• cusps

• vertical tangents (where it gets flat and weird)

slope of the tangent line equal to the slope of the secant line

f(b)-f(a) / b - a = f’(x)

estimate f’(a)

find average rate of change between two points sandwiching “a” in the table

meaning of f’(a) when looking at a table

how fast is quantity a changing at the exact moment t = 15 and is it growing or shrinking?

equation of every horizontal tangent line to the graph of g

find every y-value where slope = 0

1. find derivative

2. set derivative equal to 0 to solve for each x value

3. plug each one back into original equation to find y

4. write as: y = ___

equation of the line tangent

1. find slope

2. find y value

3. plug into pt slope form

what does “is” stand for

=

slope of the line tangent to __

derivative!!!!!!

ln (1) =

0

position to velocity

take derivative!!!