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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,

7 years ago


Answers : (1)


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+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


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7 years ago

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