Precalculus assist » introductory Calculus » Tangents come a Curve » discover the steep of a heat Tangent come a Curve at a Given allude

Find the slope of the line 

*
 at the point 
*
.

You are watching: Slope of a curve at a point


*


*


*


*


Explanation:

First find the steep of the tangent to the line by acquisition the derivative.

Using the Exponential rule we acquire the following,

*
 

 

*
.

Then plug 1 right into the equation as 1 is the suggest to discover the slope at. 

*
.


Explanation:

One means of detect the slope at a given point is by recognize the derivative. In this case, we deserve to take the derivative of y with respect to x, and plug in the wanted value for x.

*

Using the exponential rule we acquire the following derivative,

*
.

Plugging in x=2 native the point 2,3 gives us the final slope,

*

*

*

Thus our slope in ~ the details point is

*
.

Note that in this case, making use of the y coordinate was not necessary.


Explanation:

To find the slope of the tangent heat of the function at the given value, advice the an initial derivative because that the given.

The first derivative is

and for this function

*

and

*

So the steep is

*


Explanation:

To find the slope of the tangent heat of the function at the given value, evaluate the first derivative for the given value.

The very first derivative is

and because that this function

*

and plugging in the specific x value we get,

*

So the steep is

*
.


Explanation:

Calculate the derivative of 

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

The derivative is: 

*

With the offered point 

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

*

The steep of the tangent line that intersects point 

*
 is
*
.


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