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

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Answer 1 · 2016-06-16T14:12:26

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!