Suppose f(x) is continuous on [2,8] and −4≤f′(x)≤5 for all x in (2,8). use the mean value theorem to estimate f(8)−f(2).

2≤x≤8 −4≤f′(x)≤5 f is continuous in differentable on [2,8] so we know there is c btw 2 and 8 such that f′(c)=f(8)−f(2)/8−2 And we know −4≤f′(c)≤5 => we have −4≤ f(8)−f(2)/8−2 ≤5

Google it that might work

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)