Question

Using the definition of derivative, the slope of the tangent line to the parabola y=3x²+2 at the point (−1,5) is_

Answer 1

The slope of the tangent line to the parabola y=3x²+2 at the point (-1,5) is -6.

Step-by-step explanation:

To find the slope of the tangent line to the parabola y=3x²+2 at the point (-1,5), we need to find the derivative of the function and evaluate it at x=-1. The derivative of y=3x²+2 can be found using the power rule for differentiation. Applying the power rule, we get dy/dx = 6x. Evaluating this derivative at x=-1 gives us a slope of -6. Therefore, the slope of the tangent line to the parabola y=3x²+2 at the point (-1,5) is -6.