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Let f : R to R be a differentiable funct...

Let `f : R to R` be a differentiable function given by `f(x) =x^(3)-3x + 2020`. If g(x) is a continuous function defined by
`g(x) ={{:("Minimum" f(t),0 le t le x, 0 le x le 1),("Maximum" f(t), 1 lt t le x, 1 lt x le 2):}`
and m and M be the least and the greatest value of g(x) on [0,2] then which one of the following is correct?

A

M-m=2

B

m=2020

C

M=2022

D

m=2019

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x) = 3x^(2) -3`
For `0 le x le 1`, f(x) is strictly decreasing
`rArr g(x) =x^(2) - 3x + 2020, 0 le x le 1`
For `1 lt x le 2`, f(x) is strictly increasing `rArr g(x) = xp^(3) - 3x + 2020, 1 lt x le 2`
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