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Thank you for visiting For the following exercises use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing.

35. [tex]f(x) = x^4 - 4x^3 + 5[/tex]

36. [tex]h(x) = x^5 + 5x^4 + 10x^3 + 10x^2 - 1[/tex]

37. [tex]g(t) = t\sqrt{t+3}[/tex]

38. [tex]k(t) = 3t^{\frac{2}{3}} - t[/tex]

39. [tex]m(x) = x^4 + 2x^3 - 12x^2 - 10x + 4[/tex]

40. [tex]n(x) = x^4 - 8x^3 + 18x^2 - 6x + 2[/tex]

Answer :

Sure! Let's go through the solution step-by-step for the given question:

Eddie is arranging cards numbered from 1 to 10 in a row. To determine the number of possible arrangements, we need to find all the permutations of these 10 cards.

The total number of permutations of [tex]\( n \)[/tex] distinct items is given by the factorial of [tex]\( n \)[/tex], denoted as [tex]\( n! \)[/tex]. In this scenario, [tex]\( n \)[/tex] is 10.

### Step-by-step calculation:

1. Understanding Factorial:
- The factorial of a number [tex]\( n \)[/tex], denoted as [tex]\( n! \)[/tex], is the product of all positive integers less than or equal to [tex]\( n \)[/tex].
- For example, [tex]\( 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \)[/tex].

2. Calculate 10!:
- To find the number of ways to arrange 10 cards, we need to calculate [tex]\( 10! \)[/tex].
- [tex]\( 10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \)[/tex].

3. Perform the Multiplication:
- Calculate the product step by step:
- [tex]\( 10 \times 9 = 90 \)[/tex]
- [tex]\( 90 \times 8 = 720 \)[/tex]
- [tex]\( 720 \times 7 = 5040 \)[/tex]
- [tex]\( 5040 \times 6 = 30240 \)[/tex]
- [tex]\( 30240 \times 5 = 151200 \)[/tex]
- [tex]\( 151200 \times 4 = 604800 \)[/tex]
- [tex]\( 604800 \times 3 = 1814400 \)[/tex]
- [tex]\( 1814400 \times 2 = 3628800 \)[/tex]
- [tex]\( 3628800 \times 1 = 3628800 \)[/tex]

Thus, the total number of possible arrangements of the 10 cards is [tex]\( 3,628,800 \)[/tex].

Thank you for reading the article For the following exercises use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

Rewritten by : Jeany

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