Solution Introduction The derivative of a function f at x is defined in terms of a limit which may be written as f x h f

Solution Introduction The derivative of a function f at x is defined in terms of a limit which may

function f at x is defined in terms of a limit which may be written as f x h f x f x lim h h Figure

Solution Introduction The derivative of a function f at x is defined in terms of a

limit which may be written as f x h f x f x lim h h Figure

Solution Introduction The derivative of a function f at x is defined in

Solution Introduction The derivative of a

Category: | General |

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Need help with the project see attatchment below, its my first one so im hoping for answers 1 Introduction
The derivative of a function
f
at
x
is deFned in terms of a limit, which may be written as
f
?
(
x
) =
lim
h
?
0
f
(
x
+
h
)
?
f
(
x
)
h
.
±igure 1: Graph of the function
f
(
x
)=
x
x
over [0,2]. Layered on top are the tangent line
at
x
=0.6 and two secant lines corresponding to
h
=1.0 and
h
=0.5. As
h
approaches 0, the
slope of the secant line approaches the slope of the tangent line.
The expression that we take the limit of,
f
(
x
+
h
)
?
f
(
x
)
h
is interpreted as the slope of the
secant line
that goes through the points (
x
,
f
(
x
)) and
(
x
+
h
,
f
(
x
+
h
)). Then the derivative is interpreted as a slope, in this case of the
tangent line
,
deFned as the limit of the slopes of the secant lines.
We've seen that MATLAB can be used to investigate limits. Although, MATLAB doesn't
actually Fnd the limit, it suggests an answer by being close to the true answer. In this same
way, MATLAB can help us Fnd the value of the derivative of
f
(
x
) at a single point, and as a
function of
x
(many points at once.)
±igure
1
shows that graph of
f
(
x
)=
x
x
over the interval [0,2] along with three lines which go
through the point (0.6,
f
(0.
.6)). The tangent line is drawn to have slope given by
f
?
(
x
)
evaluated at 0.6. The secant lines are drawn to have slope which depends on a speciFed

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