Find the slope of the curve y = 2x³ - 8x² + 1 at the point (2,-15)

We will use the concept of differentiation in order to find the slope of the curve at the given point.

Answer: The slope of the curve y = 2x³ - 8x² + 1 at the point (2,-15) is equal to -8.

Let us see how we will use the concept of differentiation in order to find the slope of the curve at the given point.

Explanation:

We have been given the curve that is y = 2x³ - 8x² + 1

In order to find the slope of the curve at the point (2, -15) we have to find dy / dx of the curve at that point.

Hence, on differentiating the curve on both sides with respect to x we get,

dy/dx = 6x² - 16x

Now substituting the values (2, -15) in the equation of dy/dx we get the slope of the curve at the given point which is equal to -8.

Hence, the slope of the curve y = 2x³ - 8x² + 1 at the point (2,-15) is equal to 4.