Answer :

Final answer:

To find where the function f(x) = -43x4+7x3−15x2+48 is increasing, you need to find the derivative of the function, set it equal to zero, identify critical points, and then test values in the regions between these points to determine whether the function is increasing or decreasing.

Explanation:

To find the intervals where the function f(x) = -43x4+7x3−15x2+48 is increasing, we need to analyze the first derivative, which provides information about the slope of the function. We can think of a function as increasing where its slope or derivative is positive.

So, first, find the derivative of f(x). The derivative of the function, f'(x), is -172x3 + 21x2 - 30x. To understand where this derivative is positive (where the function increases) and where it is negative (where the function decreases), we set the derivative equal to zero and solve for x to find critical points.

Then, we test values in these intervals on the first derivative to determine whether the function is increasing or decreasing. For this particular function, you would need to use a numerical method or software to get a precise answer due to the complexity of the equation.

Learn more about First Derivative Analysis here:

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