Answer :

(i) The side of the square = x

⇒ The dimensions of the box are

L = 7 – 2x

B = 5 – 2x

H = x

(ii) v(x) = L × B × H

⇒ v(x) = (7 - 2x) × (5 – 2x) × (x)

⇒ v(x) = (35 + 4x^{2} -24x) × (x)

⇒ v(x) = 4x^{3} – 24x^{2} + 35x – (1)

(iii) by (1)

⇒

⇒

Similarly,

v(1) = 4(1)^{3} – 24(1)^{2} + 35(1)

⇒ v(1) = 15

And

⇒

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