Calculus Test

How to find critical points

Find the first derivative and set equal to zero to solve for the values of x. Find the values that make the first derivative undefined but don’t make the original function undefined. Usually when its a fraction.

To find the max and minn create an x and y input and output

Use the original function in the Y=

To find Vertical asymptote for quotient rule

Find the values of x that make the denominator equal to zero.

Holes

Anything that cancels in both the numerator and denominator

Horizontal asymptotes

Degree in numerator less than degree denominator than y=0

Degree in numerator equals the degree in denominator than y= divide leading coefficients

Degree in numerator is greater than degree in denominator then y= infinity or negative infinity

To find out if increasing and decreasing

create a number line using the critical points even the ones that are undefined and input f’(x) into y equals to determine values of increasing and decreasing.

Inflection point

find the second derivative and set it equal to zero to find the values of x. To find the y value to make a coordinate plug the inflection point into the original function

Finding concave up and down

Create a number line using the points of concavity even if you get a critical point number as a point of inflection use it on the number line. Then plug f’’(x) to y= and find where its negative or positive.