A region is bounded above by the curve and below by the -axis on the interval

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

A region

R(k)

is bounded above by the curve

y = 4x - x^2

and below by the

x

-axis on the interval

0 \leq x \leq k

, where

0 < k \leq 4

. The area of the region is

A(k) = \int_{0}^{k} (4x - x^2) \,dx

. For which value of

k

does

R(k)

have the greatest area? (a)

k=\dfrac{5}{2}

(b)

k=4

(c)

k=2

(d)

k=3