Precalculus help » introduce Calculus » Tangents to a Curve » discover the steep of a line Tangent to a Curve in ~ a Given point

Find the slope of the line 

*
 at the point 
*
.

You are watching: Find the slope of the line tangent to the curve


*


*


*


*


Explanation:

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

Using the Exponential ascendancy we gain the following,

*
 

 

*
.

Then plug 1 right into the equation together 1 is the suggest to uncover the slope at. 

*
.


Explanation:

One method of finding the slope at a given point is by detect the derivative. In this case, we deserve to take the derivative of y v respect to x, and plug in the desired value because that x.

*

Using the exponential rule we acquire the complying with derivative,

*
.

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

*

*

*

Thus our slope in ~ the specific point is

*
.

Note the in this case, making use of the y name: coordinates was not necessary.


Explanation:

To discover the steep of the tangent line of the function at the provided value, advice the first derivative because that the given.

The an initial derivative is

and for this function

*

and

*

So the steep is

*


Explanation:

To find the steep of the tangent heat of the function at the offered value, advice the first derivative because that the given value.

The very first derivative is

and because that this function

*

and plugging in the particular x worth we get,

*

So the steep is

*
.


Explanation:

Calculate the derivative of 

*
 by utilizing the derivative rules. The derivative role determines the slope in ~ any point of the original function.

The derivative is: 

*

With the given point 

*
*
. Instead of this worth to the derivative duty to identify the steep at that point.

*

The steep of the tangent line that intersects point 

*
 is
*
.

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