If f ( x ) = { 3 − x 2 , x ≤ 2 a + 14 − ∣ x − 48∣ , x 2 and if f ( x ) has a local maxima at x = 2 , then, the greatest value of a is

Question

If f ( x ) = { 3 − x 2 , x ≤ 2 a + 14 ​ − ∣ x − 48∣ , x > 2 ​ and if f ( x ) has a local maxima at x = 2 , then, the greatest value of a is

TestHub · Accepted Answer

Local maximum at x = 2 ⇒ ​ ⇒ h → 0 lim ​ f ( 2 + h ) ≤ f ( 2 ) ⇒ h → 0 lim ​ ( a + 14 ​ − ∣2 + h − 48∣ ) ≤ 3 − 2 2 ⇒ a + 14 ​ ≤ 45 ⇒ a ≤ 2011 ​

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