If f(x) = λ 2 x + 3 , 0 ≤ x ≤ 3 μ x + 12, 3 x ≤ 9 is differentiable at x = 3 , then the value of λ + μ is equal to

Question

If f(x) = λ 2 x + 3 , 0 ≤ x ≤ 3 μ x + 12, 3 x ≤ 9 is differentiable at x = 3 , then the value of λ + μ is equal to,

MARKS App · Accepted Answer

∵ f ( x ) is continuous at x = 3 ∴ L H L = R H L = f ( 3 ) λ 2 ( 3 ) + 3 = μ ( 3 ) + 12 ⇒ λ = μ +4 ......(1) Also f ( x ) is differentiable at x = 3 ∴ at x = 3 L H D = R H D λ 2 2 ( 3 ) + 3 · 2 = μ ⇒ λ = 3 μ ......(2) By (1) and (2) μ = 2 , λ = 6

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