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

Step-by-step solution

f^ (x)-g^ (x)=0 Integrating, f^ (x)-g^ (x)=c f^ (1)-g^ (1)=c 4-2=c c=2 f^ (x)-g^ (x)=2 ; Integrating, f(x)-g(x)=2 x+c₁ f(2)-g(2)=4+c₁ 9-3=4+c₁ c₁=2 f(x)-g(x)=2 x+2 At x=3 / 2, f(x)-g(x)=3+2=5