Question

Estimate the instantaneous rate of change of g(x) = 4x² - 6 at the point x = -1

Your answer should be accurate to at least 2 decimal places.

Answer 1

The instantaneous rate of change of a function can be estimated using the concept of the derivative. In this case, the derivative of g(x) = 4x² - 6 at x = -1 is equal to -8.

Step-by-step explanation:

To estimate the instantaneous rate of change of g(x) = 4x² - 6 at the point x = -1, we can use the concept of the derivative. The derivative of a function represents the rate at which the function is changing at a given point. To find the derivative, we take the derivative of each term in the function using the power rule.

First, we find the derivative of the term 4x², which is 8x. Then, we find the derivative of the constant term -6, which is 0. Adding these derivatives together, we get the derivative of g(x) as 8x + 0. Therefore, the instantaneous rate of change of g(x) = 4x² - 6 at x = -1 is equal to 8*(-1) + 0 = -8.