The figure below shows the derivative \( F'(x) \) of \( F \). Let \( F(0) = 0 \).[Graph depicting \( F'(x) \) is shown. The curve starts above the x-axis, peaks before \( x = 1 \), crosses the x-axis between \( x = 1 \) and \( x = 2 \), dips below, reaches a negative peak between \( x = 2 \) and \( x = 3 \), and then rises to cross the x-axis between \( x = 3 \) and \( x = 4 \).]Of the four numbers \( F(1) \), \( F(2) \), \( F(3) \), and \( F(4) \), which is largest? Which is smallest? How many of these numbers are negative?- The largest value is \( F(\_\_\_\_\_) \).- The smallest value is \( F(\_\_\_\_\_) \).

GivenThe graph of the derivative of the function is given in the question and also the function value is given F(0)=0.RequiredTo determine the largest value of the function among F(1),F(2),F(3),F(4).To determine the smallest value of the function among F(1),F(2),F(3),F(4).To determine the numbers which are negative .We know that, From the graph , it has to be determined in which interval the function is increasing or decreasing . By the help of the increasing and decreasing function , the function 's largest and smallest value is determined.It is clear that F′(x)>0 in the interval 0<x<2 for the given graph .That means the function is increasing for 0<x<2 .It is clear that F′(x)<0 in the interval 2<x<4 for the given graph.That means the function is decreasing for 2<x<4 .Therefore , the largest value is F(2)and the smallest value is F(4).Since, the rate of function is increasing for 0<x<2 is greater than the rate of function is decreasing for 2<x<4.There is no numbers for which the value is negative.Therefore , none of these numbers F(1),F(2),F(3),F(4) are negative.Therefore, The larger value is F(2).The smaller value is F(4).Therefore , none of these numbers F(1),F(2),F(3),F(4) are negative.