If 2 f x + y = f x ⋅ f y for all real x , y , where f ′ 0 = 3 and f 4 = 25 , then the value of f ′ 4 is equal to

Question

If 2 f x + y = f x ⋅ f y for all real x , y , where f ′ 0 = 3 and f 4 = 25 , then the value of f ′ 4 is equal to,

MARKS App · Accepted Answer

f ′ 4 = lim h → 0 f 4 + h − f 4 h = l i m h → 0 2 f 4 + h - 2 f 4 + 0 2 h = l i m h → 0 f 4 ⋅ f h - f 4 ⋅ f 0 2 h U s i n g 2 f x + y = f x ⋅ f y , ∀ x , y f ' 4 = f 4 2 l i m h → 0 f h - f 0 h = f 4 2 × f ' 0 = 25 2 × 3 = 37.5

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