The functions are and
.
The function is .
Apply derivative on each side with respect to .
Find .
Substitute in the
.
The function is
Apply derivative on each side with respect to .
Find .
Substitute in the above function.
(a)
\Observe the graph of and
:
and
.
Find and
.
Slope of a tangent line and
:
.
Draw a tangent line on the graph of the function .
Consider two points on the tangent line and
.
Slope of a tangent line and
:
.
Therefore .
Draw a tangent line on the graph of the function .
Consider two points on the tangent line and
.
Slope of a tangent line and
:
.
Therefore .
Substitute ,
,
and
in equation
.
.
(b)
\Observe the graph of and
:
and
.
Find and
.
Draw a tangent line on the graph of the function .
Consider two points on the tangent line and
.
Slope of a tangent line and
:
.
Therefore .
Draw a tangent line on the graph of the function .
Consider two points on the tangent line and
.
Slope of a tangent line and
:
.
Therefore .
Substitute ,
,
and
in the equation
.
.
(a) .
(b) .