Question

Let f(x)= 6x^2, find fprime(3) using the limit definition of the derivative. will be slope of the tangent line to the function of x=5?

Answer 1

Step 1:

The function is .

prime of means the first derivative of at .

First find the derivative of the function using the limit definition of derivative.

Limit definition of derivative: .

Derivative of the function is .

Step 2:

Now find prime of 3.

prime of 3 can be written as .

Substitute in the derivative of the function.

prime of 3 is 36.

Step 3:

Find the slope of the tangent line at .

Slope of the tangent is the derivative of the function at that point.

Substitute in the derivative of the function.

The slope of the tangent line at is 60.

Solution:

Derivative of the function is .

prime of 3 is 36.

The slope of the tangent line at is 60.