Determine where the absolute extrema of f(x)=-3(x^2)+7x on the interval [1,3] occur.

Question

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 	=

drwls · Answer

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.