Find the absolute maximum profit that a company can make, if the profit function is given by: p (x) = 41 - 72x - 18x²

Solution:

The profit function is given as

p (x) = 41 - 72x - 18x²

Therefore,

On differentiating wrt x, we get

p' (x) = - 72 - 36x

Now,

p' (x) = 0

⇒ -72 - 36x = 0

⇒ x = - 72/36

⇒ x = - 2

On further differentiating wrt x, we get

Also,

p" (- 2/3) = - 36 < 0

By second derivative test, x = - 2 is the point of local maxima of p.

Therefore, maximum profit

p (- 2) = 41 - 72(- 2) - 18 (- 2)²

= 41 + 144 - 72

= 113 units

Hence, the maximum profit that the company can make is 113 units

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NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.5 Question 6

Find the absolute maximum profit that a company can make, if the profit function is given by: p (x) = 41 - 72x - 18x²

Summary:

Given that the profit function is given by: p (x) = 41 - 72x - 18x²The absolute maximum profit that a company can make is 113 units