How do you find the slope of a tangent line to the graph of the function #f(x) = 5x^2 + x# at (-4, 76)?

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Answer 1 · 2016-10-08T13:25:03

The slope is the first derivative evaluated at the x coordinate. In this case it is -39.

The slope, m, of the tangent to any function is the first derivative, f'(x), evaluated at the given x coordinate, "a":

m = f'(a)

Let's compute f'(x):

f'(x) = 10x + 1

Now evaluate at x = -4:

m = 10(-4) + 1

m = -39