Explain why Rolle’s theorem is not applicable to the following funct

1.	Explain why Rolle’s theorem is not applicable to the following functions in the respective intervals.(i) f(x) = \|1/x\|, x ∈ [-1,1](ii) f(x) = tan x, x ∈ [0, π](iii) f(x) = x - 2 log x, x ∈ [2,7]
Answer» (i) f(x) = \|1/x\| f(x) is not continuous at x = 0. So Rolle’s Theorem is not applicable. (ii) f(x) = tan x f(x) is not continuous at x = π/2. So Rolle’s Theorem is not applicable. (iii) f(x) = x – 2 log x f(x) = x – 2 log x f(2) = 2 – 2 log 2 = 2 – log 4 f(7) = 7 – 2 log 7 = 7 – log 49 f(2) ≠ f(7) So Rolle’s theorem is not applicable.

Explain why Rolle’s theorem is not applicable to the following functions in the respective intervals.(i) f(x) = |1/x|, x ∈ [-1,1](ii) f(x) = tan x, x ∈ [0, π](iii) f(x) = x - 2 log x, x ∈ [2,7]

Answer»

(i) f(x) = |1/x|

f(x) is not continuous at x = 0. So Rolle’s Theorem is not applicable.

(ii) f(x) = tan x

f(x) is not continuous at x = π/2. So Rolle’s Theorem is not applicable.

(iii) f(x) = x – 2 log x

f(x) = x – 2 log x

f(2) = 2 – 2 log 2 = 2 – log 4

f(7) = 7 – 2 log 7 = 7 – log 49

f(2) ≠ f(7)

So Rolle’s theorem is not applicable.