Question Number 10039 by Gaurav3651 last updated on 21/Jan/17

  let f(x) and g(x) be twice differentiable  functions on [0,2] satisfying  f′′(x)=g′′(x), f′(1)=4, g′(1)=6,  f(2)=3 and g(2)=9. Then what is  f(x)−g(x) at x=4 equal to?

Commented byprakash jain last updated on 22/Jan/17

f′′(x)=g′′(x)  ⇒f′(x)=g′(x)+C  f′(1)=4,g′(1)=6  ⇒4=6+C⇒C=−2  f′(x)=g′(x)−2  integrating  f(x)=g(x)−2x+C_1   f(2)=3,g(2)=9  3=9−2∙2+C_1 ⇒C_1 =−2  f(x)=g(x)−2x−2  f(x)−g(x)=−2x−2  f(4)−g(4)=−2∙4−2=−10

Commented bymrW1 last updated on 22/Jan/17