Determine the slope of the following curve at the given point y = 2x3 − 8x2 + 1 at the point (2, −15)
Answer: -8 is the slope of the given curve.
Let's see the solution step by step.
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.