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The function f(x) = x2 -x -6 is
- a)minimum at x = 1/2
- b)maximum at x = 1/2
- c)minimum at x = -1/2
- d)maximum at x = -1/2
Correct answer is option 'A'. Can you explain this answer?
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The function f(x) = x2-x -6 isa)minimum at x = 1/2b)maximum at x = 1/2...
Given function:
The function is f(x) = x^2 - x - 6.
Finding the minimum/maximum:
To find the minimum or maximum of the function, we need to find the critical points. Critical points occur where the derivative of the function is equal to zero or does not exist.
Step 1: Find the derivative of the function:
f'(x) = 2x - 1
Step 2: Set the derivative equal to zero and solve for x:
2x - 1 = 0
2x = 1
x = 1/2
Step 3: Determine the nature of the critical point:
To determine whether the critical point is a minimum or maximum, we can use the second derivative test. If the second derivative is positive at the critical point, it is a minimum. If the second derivative is negative, it is a maximum.
Step 4: Find the second derivative of the function:
f''(x) = 2
Step 5: Evaluate the second derivative at the critical point:
f''(1/2) = 2
Since the second derivative is positive at x = 1/2, the critical point is a minimum.
Conclusion:
Therefore, the function f(x) = x^2 - x - 6 has a minimum at x = 1/2. The correct answer is option A.
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The function f(x) = x2-x -6 isa)minimum at x = 1/2b)maximum at x = 1/2c)minimum at x = -1/2d)maximum at x = -1/2Correct answer is option 'A'. Can you explain this answer?
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