Basic Review Of Calculus printable pdf download

BASIC REVIEW OF CALCULUS I

This review sheet discuss some of the key points of Calculus I that are essential for under-

standing Calculus II. This review is not meant to be all inclusive, but hopefully it helps you

remember basics. Please notify me if you ﬁnd any typos on this review sheet.

1. By now you should be a derivative expert. You should be comfortable with derivative

notation (f (x),

). Here is some of the main derivative rules and concepts that I

expect you to know:

n 1

) = nx

(ln(x)) =

) = e

(sin(x)) = cos(x)

(cos(x)) =

sin(x)

(sin

(x)) =

(tan(x)) = sec

(x)

(cot(x)) =

csc

(x)

(sec

(x)) =

x x

(sec(x)) = sec(x) tan(x)

(csc(x)) =

csc(x) cot(x)

(tan

(x)) =

+ 1

N D

(F S) = F S + F S

[f (g(x))] = f (g(x))g (x)

2. The derivative of a function at a point represents the slope of the tangent line at that

point. That is,

f (a) = “the slope of the tangent line to the graph of f (x) at x = a.”

We can use this to help study the behavior and the graph of f (x).

(a) f (x) > 0 exactly when f (x) is increasing.

(b) f (x) < 0 exactly when f (x) is decreasing.

3. The second derivative of a function at a point represents the concavity of the graph at

that point. A function is concave up at x = a if the graph is above the tangent line near

the point x = a. A function is concave down at x = a if the graph is below the tangent

line near the point x = a. We use the second derivative in the following way.

(a) f (x) > 0 exactly when f (x) is concave up.

(b) f (x) < 0 exactly when f (x) is concave down.

not necessarily mean that we have a point of inﬂection.

4. In many applications, we want to ﬁnd local maximum and local minimum values. In

these applications, it makes sense to look at the locations on a graph where the slope

is 0. In other words, we often use the following method to ﬁnd all locations where the

slope of the graph is 0:

(a) Find the formula for the derivative: f (x).

(b) Set this formula equal to 0 and solve for x.

Basic Review Of Calculus

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