Determine the slope of the following curve at the given point y = 2x³ − 8x² + 1 at the point (2, −15)

The slope of a line represents the ratio between the change in y-coordinate with respect to the change in x-coordinate of a given line.

Answer: -8 is the slope of the given curve.

Let's see the solution step by step.

Explanation:

Given equation: y = 2x³ − 8x² + 1

Point = (2, −15)

To determine slope, we need to differentiate the given equation

dy/dx = d/dx (2x³−8x²+1)

dy/dx = 6x² – 16x

After differentiating, we get the equation of slope.

Now, put the value of x = 2 in the equation to determine the slope.

dy/dx = 6(2)² – 16(2)

dy/dx = -8 

Thus, -8 is the slope of the given curve.