2.1-2.2 AP Calc AB

1

How many points of a function does a tangent touch?
(2.1)

Perpendicular

A normal line is ______ to the tangent line.
(2.1)

f prime of c

How to read f'(c)
(2.1)

Instantaneous

The tangent looks at the _____ rate of change, which requires the limit. So, it becomes lim(x→c) f(x)-f(c)/x-c.
(2.1)

Y-Y1 = m(X-X1)

Point slope format
(2.1)

y-f(c) = f'(c)(x-c)

Tangent equation. f'(c) is the slope, a.k.a the derivative.
(2.1)

y-f(c) = -1/f'(c)(x-c)

Normal line equation. Make sure that when you are simplifying a normal line, you simplify it beginning from this format. DO NOT take the simplified version of the tangent line and just opposite-reciprocate the slope.
(2.1)

opposite, reciprocal

Perpendicular lines have ____ and _____ slopes.
(2.1)

Orthogonal line

Another name for a normal line.
(2.1)

Physical

Average velocity is a _____ example of rate of change.
(2.1)

Average Velocity

Change in distance/change in time (often portrayed as△s/△t). You hardly ever use this.
(2.1)

Instantaneous Velocity

You take the limit of the rate of change at specific time. So, lim (t→t0)△s/△t or lim (t→t0) f(t)-f(to)/t-t0.
(2.1)

Lower-bound approximation

In a table, in order to approximate the slope/derivative, you can take the rate of exchange (rise/run) of the coordinate you are looking for and the one above (the next big one).
(2.1)

Upper-bound approximation

In a table, in order to approximate the slope/derivative, you can take the rate of exchange (rise/run) of the coordinate you are looking for and the one below (the one before it).
(2.1)

Average approximation

In a table, in order to approximate the slope/derivative, you can take the slopes you found for both the upper and lower bound and average them by summing the slopes and dividing them by two. This is the best of all approximations.
(2.1)

lim(x→c) f(x)-f(c)/x-c

Form 1 of a derivative. Used whenever you have a known x-value.
(2.2)

lim(h→0) f(x+h)-f(x)/h

Form 2 of a derivative. Used whenever you don't have any known values other than the function.
(2.2)

0

Horizontal lines have a slope of ___. So, in f(x) a horizontal line means that the derivative of those points is 0, so f'(c) has a root at these points.
(2.2)

estimating

In order to construct the rest of a f'(c) graph using f(c) only is by _____ the slope between points, you can do this through rise/run. Remember, the x-coordinates of f'(c) and f(c) are the same, but for f'(c) the y-coordinate means the derivative of f(c) at that x-point.
(2.2)

Continuity

Differentiability implies ____. So, if a function is differentiable it MUST BE continuous.
(2.2)

Differentiability

Continuity does not imply_______. So, if a function is continuous IT MAY be differentiable or IT MAY NOT.
(2.2)

Domain

The _____ of f(c) is the same as the domain of f'(c), but you must exclude the values that cause the limit of f(c) not to exist.
(2.2)

Corner

One of the three ways for lim(x→c) f(x)-f(c)/x-c not to exist. Happens when the lim approaching from the left does not equal the limit approaching from the right, which creates a ____ at (c, f(c)).
(2.2)

Vertical

One of the three ways for lim(x→c) f(x)-f(c)/x-c not to exist. Happens when the limits both equal to ∞ or -∞. This creates a _____ tangent line, which is undefined.
(2.2)

Cusp

One of the three ways for lim(x→c) f(x)-f(c)/x-c not to exist. Happens when one side of the limit is going to ∞ while the other is going to -∞. This creates a ___ and a vertical tangent line at (c, f(c)). Usually happens when an exponent is a fraction.
(2.2)

Non-differentiable

When given a piecewise function,
1. Determine what f(c) is.
2. Check that both sides of the limit exist.
If these apply and are correct, then the function is continuous. However, if they do not, then the function is not only discontinuous but also _____.
(2.2)