What is the instantaneous rate of change of the function f(x)=6x^2-x at the point (-1,7)?
a. -13
b. -5
c. 7
d. 11
f' = 12 x - 1
so what is -12 - 1
?????
To determine the instantaneous rate of change of a function at a specific point, we need to find the derivative of the function and evaluate it at the given point.
First, let's find the derivative of the function f(x). The derivative of 6x^2 is 12x, and the derivative of -x is -1. Therefore, the derivative of f(x) is f'(x) = 12x - 1.
Now, let's evaluate the derivative at the given point (-1, 7). Plug x = -1 into the derivative expression:
f'(-1) = 12(-1) - 1
= -12 - 1
= -13
So, the instantaneous rate of change of the function f(x) = 6x^2 - x at the point (-1, 7) is -13.
The correct answer is a. -13.