Answer:
 .
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Step-by-step explanation:
Differentiate each function to find an expression for its gradient (slope of the tangent line) with respect to  . Make use of the power rule to find the following:
. Make use of the power rule to find the following:
 .
.
 .
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The question states that the graphs of  and
 and  touch at
 touch at  , such that
, such that  . Therefore:
. Therefore:
 .
.
On the other hand, since the graph of  and
 and  coincide at
 coincide at  ,
,  (otherwise, the two graphs would not even touch at that point.) Therefore:
 (otherwise, the two graphs would not even touch at that point.) Therefore:
 .
.
Solve this system of two equations for  and
 and  :
:
 .
.
Therefore,  whereas
 whereas  .
.
Substitute these two values back into the expression for  and
 and  :
:
 .
.
 .
.
Evaluate either expression at  to find the
 to find the  -coordinate of the intersection. For example,
-coordinate of the intersection. For example,  . Similarly,
. Similarly,  .
.
Therefore, the intersection of these two graphs would be at  .
.