Use the graph of the given function to find any relative max

Use the graph of the given function to find any relative maxima and relative minima. f(x)=x^3-3x^2+1 A. maximum: (0,1); minimum: (2, - 3) B. no maximum or minimum C. maximum: (0,1); minimum none D. maximum: none; minimum: (2, - 3)

Solution

Answer :

From the graph we can observe that the graph changes the direction from the point ( 0 , 1 ) , that is f(0) =1

So, the relative maximum is at ( 0 , 1 ) and maximum value is f(0) = 1

and the graph changes the directions at ( 2 , - 3 ) , that is f(2) = - 3 So, the relatively minimum is at ( 2 , - 3 ) and the minimum value is f(2 ) = -3