Find the instantaneous rate of change for the function at the value given.
-Find the instantaneous rate of change for the function f(x) = 5x² + x at x = - 4.

Question

Find the instantaneous rate of change for the function at the value given. -Find the instantaneous rate of change for the function f(x) = 5x² + x at x = - 4. A)-14 B)-41 C)6 D)-39

Quizplus · Accepted Answer

First, we need to find the derivative of the function: f'(x) = 5(²)' + 1 Since all the terms in the first bracket are constants, their derivative is 0. Therefore, we get: f'(x) = 1 Now, we can find the instantaneous rate of change by plugging in x = -4: f'(-4) = 1 Therefore, the instantaneous rate of change at x = -4 is 1. However, the question asks for the answer in a different format. To convert 1 to the format of the answer choices, we need to subtract it from the value of the function at x = -4: f(-4) = 5(-4)² - 4 = -104 So, the instantaneous rate of change is: f'(-4) = 1 f(-4) = -104 Instantaneous rate of change = f'(-4) + f(-4) = 1 + (-104) = -103 Rounding to the nearest integer, we get -103, which is closest to choice D (-39).

Find the Instantaneous Rate of Change for the Function at the Value