Question

Find the slope of the tangent line to the parabola y=x^2+6x at the point (−2,−8) by using the following parameters.

Answer 1

The slope of the tangent line to the parabola at the point (-2,-8) is 2.

Step-by-step explanation:

To find the slope of the tangent line to the parabola y=x^2+6x at the point (-2,-8), we can use the derivative.

First, find the derivative of the parabola using the power rule for derivatives. The derivative of x^2 is 2x, and the derivative of 6x is 6.

So, the derivative of y=x^2+6x is dy/dx = 2x+6.

Next, substitute the x-value of the given point into the derivative equation. At x=-2, the derivative is dy/dx = 2(-2)+6 = 2.

Therefore, the slope of the tangent line to the parabola at the point (-2,-8) is 2.