Final answer:
To find critical values in calculus, you need to follow these steps: Find the derivative of the function, Solve for the values of x where the derivative is equal to zero or undefined, These values are the critical values of the function.
Step-by-step explanation:
In calculus, critical values are points where the derivative of a function is either zero or does not exist. These values are important because they help us determine where the function has maximum or minimum points, known as critical points. To find critical values in calculus, you need to follow these steps:
- Find the derivative of the function.
- Solve for the values of x where the derivative is equal to zero or undefined.
- These values are the critical values of the function.
For example, let's say we have the function f(x) = x^3 - 6x^2 + 9x. To find the critical values, we first find the derivative: f'(x) = 3x^2 - 12x + 9. Next, we solve the equation 3x^2 - 12x + 9 = 0. By factoring or using the quadratic formula, we find that x = 1 and x = 3 are the critical values of the function.