If f x = tan ⁡ x 2 ,   x ∈ 0 , π 3 , then f ′ π 4    (where, . is the greatest integer function)

Step-by-step solution

LHD :   f ' π 4 = lim h → 0 + f π 4 − h − f π 4 − h = lim h → 0 + ⁡ tan ⁡ π 4 - h 2 ⁡ - tan ⁡ π 4 2 - h = lim h → 0 + ⁡ 0 - 1 - h → ∞ ∴   f ' π 4 does not exist.