For which value of x will (x – 1)(3 – x) have its maximum?

Category: QuestionsFor which value of x will (x – 1)(3 – x) have its maximum?
Editor">Editor Staff asked 11 months ago

For which value of x will (x – 1)(3 – x) have its maximum?
 
(a) 0
 
(b) 1
 
(c) 2
 
(d) -2
 
I got this question in exam.
 
My doubt stems from Calculus Application topic in portion Application of Calculus of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

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.