Question

In which interval is the radical function f(x) = sqrt(x^2 + 2x - 15) increasing? [3, ˆž) (4, ˆž) [5, 3] (ˆž, 5] ˆª [3, ˆž)

Answer 1

The function f(x) = sqrt(x^2 + 2x - 15) is increasing in the interval (-∞, -1) ∪ (3, ∞). To find this, we first find the derivative of the function, then determine where the derivative is greater than 0.

Step-by-step explanation:

To find where the function f(x) = sqrt(x^2 + 2x - 15) is increasing, we first need to find the derivative of the function. The derivative of a function gives us the rate of change of the function, which helps us determine where the function is increasing or decreasing.

First, let's find the derivative of the given function:
f'(x) = (1/2)(x^2 + 2x - 15)^(-1/2) * (2x + 2).
Now, to find where the function is increasing, we need to find where f'(x) > 0. Solving this inequality will give us the interval in which the function is increasing. In this case, it's the interval (-∞, -1) ∪ (3, ∞).

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