Precalculus Help » Introductory Calculus » Tangents To a Curve » Find the Slope of a Line Tangent to a Curve At a Given Point

Find the slope of the line 

*
 at the point 
*
.

You are watching: Slope of a curve at a point


*


*


*


*


Explanation:

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. 

*
.


Explanation:

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.


Explanation:

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

*


Explanation:

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

*
.


Explanation:

Calculate the derivative of 

*
 by using the derivative rules. The derivative function determines the slope at any point of the original function.

The derivative is: 

*

With the given point 

*
, 
*
. Substitute this value to the derivative function to determine the slope at that point.

*

The slope of the tangent line that intersects point 

*
 is
*
.


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Hamilton College, Bachelor in Arts, Mathematics. University of Connecticut, Master of Science, Applied Mathematics.
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