Determine the maximum value of f(x) = -x^2 + 4x. (2020)
Practice Questions
Q1
Determine the maximum value of f(x) = -x^2 + 4x. (2020)
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Questions & Step-by-Step Solutions
Determine the maximum value of f(x) = -x^2 + 4x. (2020)
Step 1: Write down the function you want to maximize: f(x) = -x^2 + 4x.
Step 2: Find the derivative of the function, which tells us the slope: f'(x) = -2x + 4.
Step 3: Set the derivative equal to zero to find critical points: -2x + 4 = 0.
Step 4: Solve for x: -2x = -4, so x = 2.
Step 5: Substitute x = 2 back into the original function to find the maximum value: f(2) = -2^2 + 4(2).
Step 6: Calculate f(2): f(2) = -4 + 8 = 4.
Step 7: The maximum value of the function f(x) is 4.
Quadratic Functions – Understanding the properties of quadratic functions, including their maximum or minimum values based on the coefficient of the x^2 term.
Derivative and Critical Points – Using the first derivative to find critical points where the function may achieve maximum or minimum values.
Evaluating Functions – Calculating the function value at critical points to determine the maximum or minimum.
