Question

Use the limit definition to find the slope of the tangent line to the graph of f at the given point.

f(x)=14− x² (3,5)

Answer 1

To find the slope of the tangent line to the graph of f(x) = 14 - x² at the point (3, 5), we can use the limit definition of a derivative. The derivative of f(x) is -6.

Step-by-step explanation:

To find the slope of the tangent line to the graph of f(x) = 14 - x² at the point (3, 5), we can use the limit definition of a derivative.

The derivative of a function at a given point represents the slope of the tangent line to the graph at that point.

We can start by finding the derivative of f(x), which is given by f'(x).

The derivative of 14 is 0, and the derivative of -x² is -2x. So, f'(x) = 0 - 2x = -2x.

Now, to find the slope of the tangent line at x = 3, we substitute x = 3 into f'(x):

f'(3) = -2(3) = -6.

Therefore, the slope of the tangent line to the graph of f(x) = 14 - x² at the point (3, 5) is -6.