Answer:
Explanation:
To compare the instantaneous rate of change of the function f(x) = √3x + 4 at x = 0 and x = 4, we can calculate the derivative of the function and evaluate it at those points.
First, let's find the derivative of f(x) = √3x + 4.
Using the power rule of differentiation, the derivative of √3x is (1/2)(3x)^(-1/2) * 3 = (3/2)(√3)/(2√x) = (3√3)/(2√x).
The derivative of 4 is 0 since it is a constant.
Now, we can evaluate the derivative at x = 0 and x = 4.
For x = 0:
f'(0) = (3√3)/(2√0) = undefined
For x = 4:
f'(4) = (3√3)/(2√4) = (3√3)/(4)
Since the derivative at x = 0 is undefined and the derivative at x = 4 is a finite value, we can conclude that the instantaneous rate of change of f(x) = √3x + 4 is greater at x = 4 than at x = 0.
In other words, the function is steeper (changing at a faster rate) at x = 4 compared to x = 0.