JEE MATHEMATICS MCQ: LIMITS

1 Easy

1 of 1

Application +4 | -1

The value of

c

for which the conclusion of Lagrange's theorem holds for the function

f(x)=

\sqrt{a^2-x^2}, a>1

on the interval

[1, \mathrm{a}]

View answer and explanation

Correct option: C

\frac{\sqrt{a(a+1)}}{2}

Option C (

\frac{\sqrt{a(a+1)}}{2}

) is correct because the value of c that satisfies Lagrange's theorem for the given function and interval is

\frac{\sqrt{a(a+1)}}{2}

, found by equating the derivative at c to the average rate of change.

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