Find the absolute minimum and maximum of the function 13+2x-x^{2} on the given interval [0,5]

Question:

Find the absolute minimum and maximum of the function {eq}13+2x-x^{2} {/eq} on the given interval {eq}[0,5] {/eq}

Critical Points:

The points inside the domain of the function where the function is defined but it's first order derivative either vanishes or does not exist.

Critical points are usually either maxima or minima of the function but converge is not always true,

that means the point may be maxima or minima of the function without being a critical point.

Mathematically,

Let point {eq}c {/eq} be a critical point of any function {eq}h(x) {/eq} if one of the following is satisfied:

1. {eq}h^{\prime}(c)=0 {/eq}.

Or

2. {eq}h^{\prime}(c) {/eq} doesn't exist.

Answer and Explanation:

The given function is

{eq}13+2x-x^{2} {/eq}

and we want to find the absolute maximum and absolute minimum of the function

on the given interval...

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Finding Critical Points in Calculus: Function & Graph

from CAHSEE Math Exam: Tutoring Solution

Chapter 8 / Lesson 9
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