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For any quadratic eqn px 2 +qx+r over [ a, a+h ] , then value of c belonging to (a, a+h) in Lagrange's Mean value theorm is (a) dependent on p,q,r (b) independent of p but depends upon q,r (c) Independent of p,q but depends on r (d) independent of p,q, For any quadratic eqn px2+qx+r over [ a, a+h ] , then value of c belonging to (a, a+h) in Lagrange's Mean value theorm is (a) dependent on p,q,r (b) independent of p but depends upon q,r (c) Independent of p,q but depends on r (d) independent of p,q,
For any quadratic eqn px2+qx+r over [ a, a+h ] , then value of c belonging to (a, a+h) in Lagrange's Mean value theorm is
(a) dependent on p,q,r (b) independent of p but depends upon q,r
(c) Independent of p,q but depends on r (d) independent of p,q,
Lagrange Mean Value Theorem: Let f : [a,b] in R be a continuous function such that f : (a, b) in R is differentiable. Then, there exists c in (a, b) such that f ' (c) = [ f(b) − f(a)] / [b − a] so f '(c) = 2cp + q f(a+h) = pa2+ph2+2pah+aq+qh+r f(a)=pa2+aq+r f(a+h) - f(a) = ph2+2pah+qh so f ' (c)= ph+2pa+q = 2cp+q so , c = a + (h/2) c is independent of p,q,r -- Please feel free to post as many doubts on our disucssion forum as you can. If you find any question difficult to understand - post it here and we will get you the answer and detailed solution very quickly.We are all IITians and here to help you in your IIT JEE preparation. All the best.Regards,RameshIIT Kgp - 05 batch
Lagrange Mean Value Theorem:
Let f : [a,b] in R be a continuous function such that f : (a, b) in R is differentiable. Then, there exists c in (a, b) such that f ' (c) = [ f(b) − f(a)] / [b − a]
so f '(c) = 2cp + q
f(a+h) = pa2+ph2+2pah+aq+qh+r
f(a)=pa2+aq+r
f(a+h) - f(a) = ph2+2pah+qh
so f ' (c)= ph+2pa+q = 2cp+q
so , c = a + (h/2)
c is independent of p,q,r
--
Please feel free to post as many doubts on our disucssion forum as you can. If you find any question difficult to understand - post it here and we will get you the answer and detailed solution very quickly.We are all IITians and here to help you in your IIT JEE preparation. All the best.Regards,RameshIIT Kgp - 05 batch
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