Let f(x) and g(x) be twice differentiable functions satisfying for all , and g(2) = 3f(2) = 9. Then f(25) – g(25) is equal to: [2026]

Question

Let f(x) and g(x) be twice differentiable functions satisfying $f'' (x) = g'' (x)$ for all $x \in R$ , $f' (1) = 2 g' (1) = 4$ and g(2) = 3f(2) = 9. Then f(25) – g(25) is equal to: [2026]

Smart Achievers · Accepted Answer

(2)

We have, $f'' (x) = g'' (x)$

Integrating on both sides, we get

$f' (x) = g' (x) + c$

Put x = 1

$\Rightarrow 4 = 2 + c \Rightarrow c = 2$

$∴ f' (x) = g' (x) + 2$

Integrating on both sides, we get

f(x) = g(x) + 2x + K

Put x = 2

$\Rightarrow$ f(2) + g(2) + 4 + K

$\Rightarrow$ 3 = 9 + 4 + K

$\Rightarrow$ K = –10

$∴$ f(x) = g(x) + 2x – 10

Put x = 25

$∴$ f(25) – g(25) = 50 – 10 = 40

Solution

Q.
Let f(x) and g(x) be twice differentiable functions satisfying $f'' (x) = g'' (x)$ for all $x \in R$ , $f' (1) = 2 g' (1) = 4$ and g(2) = 3f(2) = 9. Then f(25) – g(25) is equal to: [2026]

1 20

2 40

3 –20

4 –40

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