The function f ( x ) = { ∣ x − 3∣ , ( 4 x 2 ) − ( 2 3 x ) + ( 4 13 ) , x ≥ 1 x < 1 is

Mathematics - Continuity - Differentiability Question with Solution | TestHub

MathematicsContinuity - DifferentiabilityMiscellaneous/MixedEasy2 minQB

MathematicsEasymultiple choice

The function $f (x) = {∣ x - 3∣, (\frac{x ^{2}}{4}) - (\frac{3 x}{2}) + (\frac{13}{4}), x \geq 1 x < 1$ is

Answer:

A,B,C

Solution:

$f (1 + h) = 2 = f (1 - h)$

$f (3 +) = f (3 -) = 0$

Continues at $x = 1, 3$

$f^{'} (1 +) = f^{'} (1 -) = - 1$

Not differentiable at $x = 3$

Stream:JEESubject:MathematicsTopic:Continuity - DifferentiabilitySubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

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