Question

Let f : R ® R be a function satisfying

f(x + y) = f(x) + lxy + 3x²y² for all x, y Î R. If f(3) = 4 and f(5) = 52 then f ' (x) is equal to –

• A. 10x
• B. – 10x
• C. 20x
• D. 128x

Answer 1

Answer: (B)

– 10x

Answer 2

Put x = x, y = h

f(x + h) – f(x) = lxh + 3x²h²

$\lim _ { h \rightarrow 0 }$ $\frac{f(x + h) - f(x)}{h}$ = lx

̃ f '(x) = lx

x = 3, y = 2

f(5) = f(3) + l(6) + 3(3)² (2)²

48 = 6l + 108 ̃ l = – 10

f '(x) = – 10x