You’ve now covered the basic skills you need to be able to solve and graph equations. In this lesson, you’ll practice solving equations and inequalities involving quadratics, absolute values, rational expressions, exponents, logarithms, and trigonometric functions.
Why is being able to solve equations so important for Calculus? Oftentimes, we want to know where a function (i.e., at what x-value) is equal to a certain y-value (usually 0). Depending on what this function represents, we can draw a number of conclusions. For example:
- If f(t) represents the distance you are from your home and t represents time, the values of t at which f(t) = 0 represent the time(s) during which you’re at home. The derivative of f(t)—which you recall is denoted f’(t) and gives the slope of f(t) at any point t—represents the velocity. This means that the values of t where f’(t) = 0 represent the time(s) during which you’re not moving (your velocity is 0).
- If f(q) represents the profit a company would make by producing q products (i.e., q represents the quantity), you would want to find the values of q at which f(q) is maximized (i.e., f’(q) = 0).
These examples illustrate real-life situations where you would want to know where a function and its derivative are equal to 0. These are simple functions, and oftentimes functions will be much more complex. The purpose of this lesson is to enable you to solve these complex functions.
Lesson 2: Solving equations and inequalities
- Why solve equations? 📝
- Solving equations: Quadratics
- Exercises: Solve quadratic equations
- Solving equations: Absolute values
- Exercises: Solve equations involving absolute value
- Solving equations: Polynomials
- Exercises: Solve polynomial equations
- Solving equations: Rational expressions
- Exercises: Solve equations involving rational expressions
- Solving equations: Exponents
- Exercises: Solve exponential equations
- Solving equations: Logs
- Exercises: Solve logarithmic equations
- Solving equations: Trigonometric functions
- Trig identities
- Exercises: Solve trigonometric equations
- Why solve inequalities?
- Solving inequalities
- Exercises: Solve inequalities