How do you find the equation of a line tangent to the function y=6-x^2 at (2,2)?

1 Answer
Jan 30, 2017

The equation of the line is y = -4x + 10

Explanation:

The function 6-x^2 is a polynomial, which is definitely differentiable, with y' = -2x. That -2x is also the slope of the line tangent to the graph of y at any given point x.

Since we are trying to find the tangent at (2,2), we know that the slope will be -2 * 2 = -4. So, the equation of the line is:

y = -4x + a, where a is the point at which the line intersects the y axis. To find a, simply plug in the x and y coordinates of the point:

2 = -8 + a => a = 10. The final equation is:

y = -4x + 10.