Find the Slope of a Line Tangent to a Curve At a Given Point - Pre-Calculus

One way of finding the slope at a given point is by finding the derivative. In this case, we can take the derivative of y with respect to x, and plug in the desired value for x.

Using the exponential rule we get the following derivative,

.

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

Thus our slope at the specific point is .

Note that in this case, using the y coordinate was not necessary.

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

The first derivative is

and for this function

and

So the slope is

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

The first derivative is

and for this function

and plugging in the specific x value we get,

So the slope is

.

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

The derivative is:

With the given point , . Substitute this value to the derivative function to determine the slope at that point.

The slope of the tangent line that intersects point is .