Deternime the instantaneous rate of change at x=2 for:

y=x-2x^3

take the derivative

dy/dx = 1 - 6x^2

sub in the value of x=2

To determine the instantaneous rate of change at x = 2 for the function y = x - 2x^3, we need to calculate the derivative of the function and then evaluate it at x = 2.

Step 1: Find the derivative of the function.
To find the derivative of y = x - 2x^3, we differentiate each term of the function separately using the power rule:

For the term "x," the derivative is 1.
For the term "-2x^3," the derivative is -6x^2.

Putting these derivatives together, we get:

dy/dx = 1 - 6x^2

Step 2: Evaluate the derivative at x = 2.
Substituting x = 2 into the derivative, we get:

dy/dx = 1 - 6(2)^2
= 1 - 6(4)
= 1 - 24
= -23

Therefore, the instantaneous rate of change at x = 2 for y = x - 2x^3 is -23.