Let a , b ∈ R be such that the function f given by f ( x ) = ln ∣ x ∣ + b x 2 + a x , x  = 0 has extreme values at x = − 1 and x = 2 . Statement 1: f has local maximum at x = − 1 and at x = 2 . State

Question

Let a , b ∈ R be such that the function f given by f ( x ) = ln ∣ x ∣ + b x 2 + a x , x  = 0 has extreme values at x = − 1 and x = 2 . Statement 1: f has local maximum at x = − 1 and at x = 2 . Statement 2: a = 2 1 ​ and b = 4 − 1 ​

TestHub · Accepted Answer

f ′ ( x ) = x 1 ​ + 2 b x + a f has extremevalues and differentiable ⇒ f ′ ( − 1 ) = 0 ⇒ a − 2 b = 1 f ′ ( 2 ) = 0 ⇒ a + 4 b = − 2 1 ​ ⇒ a = 2 1 ​ , b = − 4 1 ​ f ′′ ( − 1 ) , f ′′ ( 2 ) are negative. f has local maxima at − 1 , 2

Mathematics - Application of Derivative Question with Solution | TestHub

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