Let f(a)>0, and let f(x) be a nondecreasing continuous function in [a,b]. Then 1 b-a _a^b f(x) ,dx has the

JEE Advanced Mathematics question

Let , and let be a nondecreasing continuous function in . Then has the

Answer: (A),(B)

nondecreasing on . Integrating over :

f(a)(b-a) f(x) dx f(b)(b-a)\ ⇒\ f(a)1{b-a} f(x) dx f(b),

with equality at either end when is constant. So the mean value has maximum and minimum : (a),

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Question ID VK-109575