Precalculus assist » introductory Calculus » Tangents to a Curve » uncover the slope of a line Tangent to a Curve in ~ a Given suggest

Find the slope of the line 

*
 at the point 
*
.

You are watching: Estimate the slope of the curve at the indicated point


*


*


*


*


Explanation:

First find the slope of the tangent come the line by acquisition the derivative.

Using the Exponential dominance we get the following,

*
 

 

*
.

Then plug 1 right into the equation together 1 is the point to find the slope at. 

*
.


Explanation:

One method of recognize the slope in ~ a given suggest is by detect the derivative. In this case, we deserve to take the derivative the y v respect to x, and plug in the wanted value because that x.

*

Using the exponential dominance we gain the following derivative,

*
.

Plugging in x=2 native the suggest 2,3 offers us the last slope,

*

*

*

Thus ours slope at the specific point is

*
.

Note that in this case, using the y coordinate was no necessary.


Explanation:

To find the slope of the tangent heat of the function at the given value, evaluate the very first derivative because that 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 provided value, evaluate the an initial derivative because that the provided value.

The first derivative is

and for this function

*

and plugging in the details x worth we get,

*

So the steep is

*
.


Explanation:

Calculate the derivative of 

*
 by using the derivative rules. The derivative function determines the slope at any suggest of the initial function.

The derivative is: 

*

With the given point 

*
*
. Instead of this worth to the derivative role to determine the slope at the point.

*

The slope of the tangent line that intersects point 

*
 is
*
.

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Pennsylvania State University-Main Campus, Bachelor of Science, chemical Engineering. Carnegie Mellon University, physician of P...
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