Final answer:
The function f(x) = ₀∫ˣ (16−t²) eᵗ² dt is increasing on the interval (-4, 4). This is determined by finding the derivative of the given function and identifying where the derivative is greater than zero.
Step-by-step explanation:
To find the largest interval of an increasing function such as f(x) = ₀∫ˣ (16−t²) eᵗ² dt, we have to first derive its derivative. Unfortunately, in this particular case, the definition of f(x) is an integral form known as a Leibniz integral.
According to the Leibniz rule, the derivative of this function f'(x) is given as f'(x) = (16 - x²) * eˣ². From the derivative formula, we can now find where f'(x) > 0 to identify the interval where f(x) is increasing.
When we solve the inequation f'(x) > 0, we find that the function is increasing on the interval (-4, 4).
Learn more about Increasing Interval