Exploring Maximum Values: Finding the Peak of a Rational Function

In mathematics, finding the maximum value of a function is a common and intriguing problem. In this blog post, we'll explore how to determine the maximum value of the function  `E=\frac{48}{p^2-2p+3}`. where `p` is a real number. Let's dive into the details and solve this problem step-by-step.

What is the maximum value of `E` if `p` is real number?

`E=\frac{48}{p^2-2p+3}`.

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Answer: 24
Explanation: 

• First, observe the numerator is constant.
• Then, observe that quadric expression,
• The maximum value of E, we need to minimize the denominator. (E is inversely proportional to     denominator
• Let's say denominator `\phi(p)=p^2-2p+3`.
  It has critical point of' `\phi'(p)=2p-2=0\implies p=1`.
• denominator has minimum when `p = 1`.
• `E` has maximum where `p = 1`.