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Find the maximum value of f(x) = -x^2 + 4x.
Find the maximum value of f(x) = -x^2 + 4x.
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Practice Questions
1 question
Q1
Find the maximum value of f(x) = -x^2 + 4x.
4
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10
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The vertex form gives maximum at x = 2. f(2) = -2^2 + 4*2 = 4.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the maximum value of f(x) = -x^2 + 4x.
Solution:
The vertex form gives maximum at x = 2. f(2) = -2^2 + 4*2 = 4.
Steps: 8
Show Steps
Step 1: Identify the function you need to analyze, which is f(x) = -x^2 + 4x.
Step 2: Recognize that this is a quadratic function in the form of ax^2 + bx + c, where a = -1, b = 4, and c = 0.
Step 3: Since the coefficient of x^2 (a) is negative, the parabola opens downwards, meaning it has a maximum point.
Step 4: To find the x-coordinate of the vertex (maximum point), use the formula x = -b/(2a). Here, b = 4 and a = -1.
Step 5: Calculate x = -4/(2 * -1) = -4/-2 = 2.
Step 6: Now, substitute x = 2 back into the function to find the maximum value: f(2) = -2^2 + 4*2.
Step 7: Calculate f(2) = -4 + 8 = 4.
Step 8: Therefore, the maximum value of f(x) is 4.
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