Given f'(x) = (x-4)(4-2x), find the x-coordinate for relative maximum on the graph of f(x)

The coordinate of the relative maximum is x=4.

Step-by-step explanation:

Given that the derivative of the function is , the maxima and minima or the critical points can be found where that is:

The solutions to this equation are and

Now, if the second derivative for a function  is negative at a critical point, then the critical point is the relative maximum.

Therefore we want to see at which of the two critical points is negative. The second derivative is:

Now is , and is , therefore we deduce that the relative maxium is located at , because there the second derivative is negative.

answer: 590

step-by-step explanation: