Determine the critical points of the function f(x) = x^2 - 4x + 4. (2022)
Practice Questions
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Determine the critical points of the function f(x) = x^2 - 4x + 4. (2022)
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Questions & Step-by-Step Solutions
Determine the critical points of the function f(x) = x^2 - 4x + 4. (2022)
Step 1: Start with the function f(x) = x^2 - 4x + 4.
Step 2: Find the derivative of the function, which is f'(x). The derivative of x^2 is 2x, and the derivative of -4x is -4. So, f'(x) = 2x - 4.
Step 3: Set the derivative equal to zero to find critical points. This means we solve the equation 2x - 4 = 0.
Step 4: Solve for x. Add 4 to both sides: 2x = 4. Then divide both sides by 2: x = 2.
Step 5: The critical point is x = 2.
Critical Points – Critical points occur where the derivative of a function is zero or undefined, indicating potential local maxima, minima, or points of inflection.
Derivative Calculation – Finding the derivative of a function is essential for determining critical points.
Setting Derivative to Zero – To find critical points, the derivative must be set to zero and solved for x.
