To find the absolute maximum and minimum values of the function f(x) = 2 – x² over the interval [-1, 1], we can follow a systematic approach that includes checking the endpoints of the interval as well as any critical points within the interval. Step 1: Identify the Critical Points A critical point occurs where … Read more
The discriminant is a crucial part of solving quadratic equations, given by the formula: D = b² – 4ac, where ax² + bx + c = 0. For the quadratic equation in question, x² – 4x + 2 = 0, the coefficients are: a = 1 b = -4 c = 2 Now, substituting these … Read more
Understanding Discontinuity in Functions Discontinuity in a function arises when the function fails to meet certain criteria at a specific point. For a function to be continuous at a point ‘a’, it must satisfy three main conditions: The function is defined at ‘a’. The limit of the function as it approaches ‘a’ must exist. The … Read more
Comparing an improper fraction to a proper fraction may seem tricky at first, but it’s quite straightforward once you understand the definitions of both types of fractions. Let’s break it down step by step. Definitions A proper fraction is a fraction where the numerator (the top number) is less than the denominator (the bottom number). … Read more
The mean IQ of 112 and standard deviation of 20 provide significant insights into the cognitive capabilities of the population being studied. When conducting a market research campaign, analyzing these statistics can help in understanding the demographic’s behavior, preferences, and purchasing power. In this context, the mean IQ score signifies that the average cognitive aptitude … Read more
In probability theory, two events A and B are considered mutually exclusive when they cannot both occur at the same time. In other words, if event A happens, then event B cannot happen, and vice versa. Let’s delve a bit deeper into this concept. The probability of the intersection of two events, denoted as P(A … Read more
To simplify the expression 3 + 4y + 3 + 7y, you’ll want to combine the like terms, which are those that have the same variable component. 1. **Identify like terms:** The terms can be broken down into two categories: – Constant terms: 3 and 3 – Variable terms: 4y and 7y 2. **Combine the … Read more
Determining the number of roots of a polynomial can actually be done relatively quickly by observing a few key characteristics of the equation. Here’s a detailed breakdown of the steps you can take: Identify the Degree of the Polynomial: The first step is to look at the highest power of the variable in the polynomial … Read more
To find the equation of the tangent line to the curve defined by y = 4x – 3x² at the point (2, 4), we follow these steps: Find the derivative: The derivative of a function gives us the slope of the tangent line at any point on that curve. Let’s find the derivative of the … Read more
To check the sum of the numbers 27, 15, and 12, you simply add these three numbers together. Here’s how you can do it step by step: Start by adding the first two numbers: 27 and 15. 27 + 15 = 42 Next, take the result from the previous addition (42) and add the third … Read more