Question

$f(x)$ and $g(x)$ are two differentiable functions on $[0, 2]$ such that $f " (x) - g"(x) = 0,
f '(1) = 2g'(1) = 4, f(2) = 3g(2) = 9$ then $f (x)-g(x)$ at $x = 3/2$ is

• A. 0
• B. 2
• C. 10
• D. 5

Answer 1

Answer: (D)

$\because \:f ''(x) - g " (x) = 0$
Integrating, $f ' (x) - g' (x) = c;$
$\Rightarrow \:\: f ' (1)- g' (1) = c \Rightarrow 4 - 2 = c \Rightarrow c = 2$.
$\therefore \:\:f' (x) - g' (x) = 2;$
Integrating, $f (x) - g (x) = 2x + c_1$
$\Rightarrow \:\:\: f (2) - g(2) = 4 + c_1 \Rightarrow 9 - 3 = 4 + c_1$;
$\Rightarrow \: c_1 = 2 \therefore f (x) - g(x) = 2x + 2$
At $x = 3/2, f (x) - g(x) = 3 + 2 = 5.$