posted by Salman on .
Determine where the absolute extrema of f(x)=-3(x^2)+7x on the interval [1,3] occur.
1. The absolute maximum occurs at =
2. The absolute minimum occurs at =
Set the derivative f'(x) = 0 and solve for x.
-6x + 7 = 0
x = 7/6
Since the second derivative f"(x) = -6, the extremum at x = 7/6 is a maximum. The minimum for the interval [1,3] will occur at x = 3, since the f(x) just keeps getting lower for higher values of x when x > 7/6.