How do you find the slope of a tangent line to the graph of the function #y = 4x^2 -4x -20 # at x=3?

Question

Cameron Alexander · Accepted Answer

First, differentiate.

We can do this by the power rule, which states if #y = x^n," then "y' = nx^(n - 1)#. Calculating: #y' = 8x - 4# The slope of the tangent is given by substituting your #x# value into the derivative function and evaluating. #y' = 8(3) - 4# #y' = 20# Hence, the slope of the tangent is #20# at the point #x = 3#. Hopefully this helps!

Axel Alvarez · Answer

undefined To find the slope of a tangent line to the graph of a function at a specific point, you can use the derivative of the function.

To find the derivative of the function y = 4x^2 - 4x - 20, you can apply the power rule.

The power rule states that if you have a function of the form f(x) = ax^n, where a and n are constants, the derivative is given by f'(x) = nax^(n-1).

Applying the power rule to the function y = 4x^2 - 4x - 20, we get y' = 8x - 4.

To find the slope of the tangent line at x = 3, substitute x = 3 into the derivative equation:

y' = 8(3) - 4 = 24 - 4 = 20.

Therefore, the slope of the tangent line to the graph of the function y = 4x^2 - 4x - 20 at x = 3 is 20.