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3. Which is greater: the instantaneous rate of change of f(x) = √3x + 4 at x = 0 or at x = 4? How

do you know?

User Subbu M
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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.

User Andrei Amariei
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