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For which value of x will (x – 1)(3 – x) have its maximum?(a) 0(b) 1(c) 2(d) -2I got this question in exam.My doubt stems from Calculus Application topic in portion Application of Calculus of Mathematics – Class 12

Answer»

Correct answer is (c) 2

The explanation: LET, y = (x – 1)(3 – x) = 4X – x^2 – 3

Then, dy/dx = 0

Or 4 – 2x = 0

Or 2x = 4

Or x = 2

Now, [d^2y/dx^2] = -2 which is negative.

Therefore, (x – 1)(3 – x) will have its maximum at x = 2.



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