Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
I need some help figuring out 98 and 99 I am struggling. Thank you.
![## Understanding Intermediate Value Theorem
**Using the Intermediate Value Theorem:**
In Exercises 89-94, use the Intermediate Value Theorem and an appropriate utility to approximate the zero of the function in the interval \([a, b]\). Repeatedly "zoom in" on the graph of the function to approximate the zero to two decimal places. Use the appropriate feature of your calculator to help approximate the zero accurate to four decimal places.
### Exercises:
**89.** \( f(x) = x^3 - x + 1 \)
Interval: \([-2, -1]\)
**90.** \( f(x) = x^3 - x + \frac{1}{2} \)
Interval: \([-1, 0]\)
**91.** \( f(x) = x^7 + 2x^6 - 4x^5 - 3x^4 + 3 \)
Interval: \([-3, -2]\)
**92.** \( f(x) = x^6 + 2x^4 - 5x^2 - 3 \)
Interval: \([0, 1]\)
**93.** \( f(x) = x^3 + 2x^2 + 3x - 4 \)
Interval: \([0, 1]\)
### Proof of the Intermediate Value Theorem
**94.** Using the Intermediate Value Theorem in Exercise 93, verify that the Intermediate Value Theorem applies to the indicated interval and find the value of \( c \) guaranteed by the theorem.
### Functions and Intervals
**95.** \( f(x) \)
Interval: \([0.5, 1]\)
\( f(x) = 11 \)
**96.** \( f'(x) \)
Interval: \([0, 3]\)
\( f'(x) = 3 \)
**97.** \( f(x) = e^{-x} - \sin x \)
Interval: \([1, 2]\)
**98.** \( f(x) = 6x^3 + x^2 + 2 \)
\( f'(2) = 6 \)
**99.** \( f(x) = \sqrt{16 - 2x} \)
\( f'(4) = 3 \)
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