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Given f(x) = 4- ((1)/(2) - x)^(2//3) , g...

Given `f(x) = 4- ((1)/(2) - x)^(2//3) , g(x) = {:{((tan[x])/(x),","x cancel(=)0),(1,","x=0):}" "h(x)={x}, k (x) = 5^(log_(2)(x+3))`
Then in [0,1], Lagrange's mean value theorem is not applicable to (where [.] and {.} represents the greatest integer functions and fractions part functions, respectively )

A

f

B

g

C

k

D

h

Text Solution

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The correct Answer is:
A, B, D
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Knowledge Check

  • Let f(x)=([a]^(2)-5[a]+4)x^(3)-(6{a}^(2)-5{a}+1)x-(tan x) xx sin x be an even function for all x in R . Then the sum of all possible values of a is (where [.] and {.} denote gretest integer function and fractional part function, respectively )

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  • Let f(x)=(x^(2)+1)/([x]).1lexle3.9 . [.] denotes the greatest integer function Then

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    f(x) is monotonically decreasing in [1,3.9]
    B
    f(x) is monotonically increasing in [1,3.9]
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    the greatest value of f(x) is `(1)/(3)xx16.21`
    D
    the least value of f(x) is 2.

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