Question

10. Verify Lagrange's Mean value Theorem for the function f(x) = x³+x²-6x
on (-1,4)​

Answer 1

Since f(x) is differentiable on all intervals, we can choose any two points (Here we take 11 and 3). So from the mean value theorem, we have some c such that

F′(c)=(f(11)−f(3))/11−3)

Now given 5⩽F′(c)⩽14 therefore 5⩽(f(11)−f(3))/8⩽14

=> 40⩽(f(11)−f(3))⩽112

Hence a = 112 and b = 40 which gives a+b = 152 as the answer.