Let be continuous on and differentiable on with for all in

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Let

g

be continuous on

[2,7]

and differentiable on

(2,7)

with

|g'(x)|\le 6

for all

x

(2,7)

. Which of the following must be true? (a)

|g(7)-g(2)|\le 6

(b) There exists

c\in(2,7)

such that

|g'(c)|=6

(c)

|g(7)-g(2)|\le 30

(d)

|g(7)-g(2)|=30