what is the best estimate of the instantaneous rate of change for the function f(x)= -4x^2 at the point (-1/2, -1)
1. 4
2. -3/4
3. 8
4. -3
one estimate would be
(f(0)-f(-1))/(0-(-1)) = (0+4)/1 = 4
To find the instantaneous rate of change for the function f(x) = -4x^2 at the point (-1/2, -1), we need to find the derivative of the function and evaluate it at that point.
Step 1: Find the derivative of f(x) = -4x^2.
To find the derivative, we can use the power rule, which states that if f(x) = ax^n, then f'(x) = nax^(n-1).
Applying the power rule to f(x) = -4x^2, we get: f'(x) = -4 * 2x^(2-1) = -8x.
Step 2: Evaluate the derivative at the point (-1/2, -1).
To evaluate the derivative at (-1/2, -1), we substitute x = -1/2 into f'(x) = -8x.
f'(-1/2) = -8 * (-1/2) = 4.
Therefore, the best estimate of the instantaneous rate of change for the function f(x) = -4x^2 at the point (-1/2, -1) is 4.
So, the correct answer is option 1.