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Find the value of k such that the function f(x) = x^2 + kx has a maximum at x =
Find the value of k such that the function f(x) = x^2 + kx has a maximum at x = -2.
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Practice Questions
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Q1
Find the value of k such that the function f(x) = x^2 + kx has a maximum at x = -2.
-4
-2
0
2
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For a maximum, f'(x) = 2x + k = 0 at x = -2. Thus, k = 4.
Questions & Step-by-step Solutions
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Q
Q: Find the value of k such that the function f(x) = x^2 + kx has a maximum at x = -2.
Solution:
For a maximum, f'(x) = 2x + k = 0 at x = -2. Thus, k = 4.
Steps: 7
Show Steps
Step 1: Start with the function f(x) = x^2 + kx.
Step 2: To find the maximum, we need to find the derivative of f(x). The derivative f'(x) is calculated as f'(x) = 2x + k.
Step 3: We want to find the value of k such that the maximum occurs at x = -2.
Step 4: Substitute x = -2 into the derivative: f'(-2) = 2(-2) + k.
Step 5: Simplify the equation: f'(-2) = -4 + k.
Step 6: For a maximum, the derivative must equal 0. So, set -4 + k = 0.
Step 7: Solve for k: k = 4.
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