m150a Lab notes for assign 2.htm

Mathematics 150 AL

Notes for Assignment 2

Definition: A function $\ f$ defined on () is differentiable at a point in () if

exists.

This limit is denoted by $\ f\prime (x)$ .

is called the difference quotient of :

Example:

Let

Define f using the definition option. Then use the evaluate option to determine

MATH

go to "compute", then "expand"

and evaluate the limit as $h\rightarrow 0;$

Tangent lines: If the derivative of a function exists at a point , then it

is equal to the slope of the tangent line of this function. Moreover, the equation

of the tangent line at this point is given by

Example: Let $f(x)=\sin x$ , then at $a=\pi /2$ we can compute $f^{\prime }:$

The tangent line at this point is given by

or

We can plot the graph of the function and the tangent line at $\pi /2$ :

plot $\ \ \ \ \sin x$

on the same graph, plot

m150a Lab notes for assign 2__33.png

$f(x)=\sin x$ , tangent line to

at x=

$\frac{\pi }{2}$ ,

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