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

Question

5984 views around the world

You can reuse this answer
Creative Commons License

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

How do you find the slope of a tangent line to the graph of the function f(x) = 5x^2 + xf(x)=5x2+xf(x) = 5x^2 + x at (-4, 76)?