How do you find the slope and the equation of

Cierra Woodard

Cierra Woodard

Answered question

2022-02-12

How do you find the slope and the equation of the tangent line to the graph of the function at the given value of x for f(x)=x413x2+36 at x=2?

Answer & Explanation

Keely House

Keely House

Beginner2022-02-13Added 13 answers

Explanation:
First of all, the slope is given by the derivative, so you have that
f(x)=4x326x, and thus f'(2)=32-52=-20
Also, we know that the tangent line must pass across the point 2, f(2), namely (2,0)
If you know that a line has slope m, and crosses the point (x0,y0), then you obtain its equation with the formula
yy0=m(xx0). Plugging the values, we have
y=-20(x-2), which we can rearrange into y=-20x+40

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?