Precalculus : Find the Slope of a Line Tangent to a Curve At a Given Point
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Example Questions
Example Question #1 : Tangents To A Curve
Find the slope of the line 
First find the slope of the tangent to the line by taking the derivative.
Using the Exponential Rule we get the following,
Then plug 1 into the equation as 1 is the point to find the slope at.
Example Question #2 : Tangents To A Curve
Find the slope of the following expression at the point
One way of finding the slope at a given point is by finding the derivative. In this case, we can take the derivative of y with respect to x, and plug in the desired value for x.
Using the exponential rule we get the following derivative,
Plugging in x=2 from the point 2,3 gives us the final slope,
Thus our slope at the specific point is 
Note that in this case, using the y coordinate was not necessary.
Example Question #1 : Find The Slope Of A Line Tangent To A Curve At A Given Point
Find the slope of the tangent line of the function at the given value
at
To find the slope of the tangent line of the function at the given value, evaluate the first derivative for the given.
The first derivative is
and for this function
and
So the slope is
Example Question #1 : Find The Slope Of A Line Tangent To A Curve At A Given Point
Find the slope of the tangent line of the function at the given value
at
To find the slope of the tangent line of the function at the given value, evaluate the first derivative for the given value.
The first derivative is
and for this function
and plugging in the specific x value we get,
So the slope is
Example Question #1 : Find The Slope Of A Line Tangent To A Curve At A Given Point
Consider the function 
Calculate the derivative of 
The derivative is:
With the given point 
The slope of the tangent line that intersects point 
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