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

First, differentiate.

Calculating:

Hopefully this helps!

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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.

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