Given the values of the derivative fx in the table and that

Given the values of the derivative f\'(x) in the table and that f(0) = 180, estimate the values below. Find the best estimates possible (average of the left and right hand sums).

Solution

As given in question f(0) = 180 and the table as:

x => 0 2 4 6

f \'(x) => 7 14 21 28

hence from the table the estimates possible are:

f(2)= 14*2 + 180 = 208
f(4)= 21*4 + 180 = 264
f(6)= 28*6 + 180 = 348