Calc Midterm 2

Front 1

What is a critical value?

Back 1

A critical value of a function f is any number c in the domain of f for which the tangent line at (c, f (c)) is horizontal or for which the derivative does not exist. When x=0

Front 2

Which limit statements show that there are vertical asymptotes?

Back 2

lim f(x)=∞ x→a−. or lim f (x)= ∞ x→a+
or
lim f(x)=−∞ or x→a−. or lim f (x)= −∞. x→a+

Front 3

The graph of a rational function _____ crosses a
vertical asymptote

Back 3

never

Front 4

In an expression, if the variable "a" makes the expression =0, what is the vertical asymptote?

Back 4

x=a

Front 5

What two limit statements need to be true for a horizontal asymptote to occur?

Back 5

lim f(x)=b x→−∞
or
lim f (x)= b. x→∞

Front 6

A linear asymptote that is neither vertical nor
horizontal is called a _____

Back 6

slant

Front 7

When the degree of the numerator is less
than the degree of the denominator, what is the y-intercept

Back 7

Y is equal to 0

Front 8

How do you find a slant asymptote?

Back 8

Divide the numerator by the

Front 9

Define absolute minimum

Back 9

f (c) is an absolute minimum if f (c) ≤ f (x) for all x in I.

Front 10

Define Absolute maximum

Back 10

f (c) is an absolute maximum if f (c) ≥ f (x) for all x in I.