please help answer these question. thank you. ### Calculus Optimization Problems#### 1. Absolute Minimums and Maximums**Problem:**Find the absolute minimums and maximums of the following function on the given intervals:\[ f(x) = x^2 - 6x + 5 \, \text{on} \, [-2, 5] \]**Solution Approach:**To solve this, you'll need to perform the following steps:1. Find the critical points by setting the first derivative, $ f'(x) $, equal to zero.2. Evaluate the function $ f(x) $ at the critical points and the end points of the interval.3. Compare these values to determine the absolute minimum and maximum values.#### 2. Optimal Dimensions for a Pen**Problem:**You have 120 feet of fencing to construct a pen with 4 equal-sized stalls. If the pen is rectangular and shaped like the one below, what are the dimensions of the pen of the largest area and what is that area?**Diagram:**The diagram shows a rectangular pen divided into 4 equal-sized stalls, aligned horizontally.**Solution Approach:**To solve this, consider:1. Express the area $ A $ of the rectangular pen in terms of its length $ l $ and width $ w $.2. Use the constraint given by the perimeter (fencing available) to write an equation relating $ l $ and $ w $.3. Substitute this constraint into the area equation to express $ A $ as a function of a single variable.4. Use calculus to find the maximum area by taking the derivative of $ A $ with respect to the chosen variable and finding the critical points.#### 3. Revenue and Cost Optimization**Problem:**Consider a pizzeria that sells pizzas for a revenue of:\[ R(x) = 10x \]and a cost of:\[ C(x) = 2x + 0.2x^2 \]dollars. How many pizzas sold maximizes the profit?**Solution Approach:**To solve this problem:1. Establish the profit function $ P(x) = R(x) - C(x) $.2. Take the derivative of $ P(x) $ to find the critical points that will help in maximizing the profit.3. Analyze these critical points by evaluating the second derivative or using the first derivative test to determine if they correspond to a maximum profit

As per our guideline we are supposed to answer only first question of a multiple type of questions.…

Answered: . Find the absolute the following…

. Find the absolute the following functions on f(x) = x² - 6x + 5 minimums the and maximums of given intervals on [-2,5]

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section: Chapter Questions

Problem 30P: In this problem you are asked to find a function that models in real life situation and then use the...

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