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
It was -13
well, it's 12x-1 everywhere, so ...
To find the instantaneous rate of change of a function at a specific point, we need to find the derivative of the function and then evaluate it at that point.
First, let's find the derivative of the function f(x)=6x^2-x. The derivative gives us the rate of change of the function at any point.
Using the power rule, we differentiate each term of the function:
f'(x) = (2*6)x^(2-1) - 1*(1) = 12x - 1
So the derivative of f(x) is f'(x) = 12x - 1.
Now that we have the derivative, we can substitute the x-coordinate of the given point (-1,7) into the derivative function f'(x) to find the instantaneous rate of change at that point:
f'(-1) = 12(-1) - 1 = -12 - 1 = -13
Therefore, the instantaneous rate of change of the function f(x) = 6x^2-x at the point (-1,7) is -13.
Hence, the correct answer is A. -13.