Let m and n be the number of points at which the function f ( x ) = max { x , x 3 , x 5 , … . , x 21 } , x ∈ R , is not differentiable and not continuous, respectively. Then m + n is equal to ________

Question

Let m and n be the number of points at which the function f ( x ) = max { x , x 3 , x 5 , … . , x 21 } , x ∈ R , is not differentiable and not continuous, respectively. Then m + n is equal to ________ .

TestHub · Accepted Answer

f ( x ) = ⎩ ⎨ ⎧ ​ x , x 21 , x , x 21 , ​ x < − 1 − 1 ≤ x < 0 0 ≤ x < 1 x ≥ 1 ​ f ( x ) is continuous everywhere. ​ ∴ n = 0 f ′ ( x ) = ⎩ ⎨ ⎧ ​ 1 , 21 x 20 , 1 , 21 x 20 , ​ x < − 1 − 1 ≤ x < 0 0 < x < 1 x ≥ 1 ​ ​ ∴ f ( x ) is non-differentiable at x = − 1 , 0 , 1 ​ ∴ m = 3 m + n = 3 ​

Mathematics - Continuity - Differentiability Question with Solution | TestHub

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