Find the slope of the line
You are watching: Find the slope of the line tangent to the curve
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.
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.
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
So the steep is
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
Calculate the derivative of
The derivative is:
With the given point
The steep of the tangent line that intersects point
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