Find the slope of the line
You are watching: Slope of a curve at a point
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.
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.
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
So the steep is
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
Calculate the derivative of
The derivative is:
With the offered point
The steep of the tangent line that intersects point
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