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in[0,2] f(x) and g(x) are differentiable functions with f`(1)=2, g`(1)=4 ,f(2)=3 ,g(2)=9 then at x=3/2 find value of f(x)-g(x)

in[0,2] f(x) and g(x) are differentiable functions with f`(1)=2, g`(1)=4 ,f(2)=3 ,g(2)=9 then at x=3/2 find value of f(x)-g(x)

Grade:12th pass

1 Answers

Pradeep Tangirala
73 Points
3 years ago
f'(1)=2   so...f'(x) = 2x (say)
Integrating on both sides...
So f(x)=2x + C
Where C is some constant that we can find...
But f(2)=3
So f(2)=2×2 +c
4+C=3
C=-1
So...f(x)= 2x-1
f(3/2)=2×3/2 - 1
            =2
Similarly....g(x)=4x + k
          g(2)=9
So...K=1
g(x)=4x+1
g(3/2)=4×3/2 +1
           =7
 
So...f(x) - g(x) = 2-7 =-5

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