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The function f(x) = 2x - x2 + 3 has
  • a)
    a maxima at x = 1 and a minima atx = 5
  • b)
    a maxima at x = 1 and a minima at x = -5
  • c)
    only a maxima at x = 1
  • d)
    only a minima at x = 1
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The function f(x) = 2x - x2 + 3 hasa)a maxima at x = 1 and a minima at...

So at x = 1 we have a relative maxima.
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Most Upvoted Answer
The function f(x) = 2x - x2 + 3 hasa)a maxima at x = 1 and a minima at...


Explanation:

Finding Critical Points:
To find the critical points of the function f(x), we need to find where the derivative of the function is equal to 0.
Given f(x) = 2x - x^2 - 3, we find the derivative f'(x) = 2 - 2x.

Setting f'(x) = 0, we get:
2 - 2x = 0
2 = 2x
x = 1

Classifying Critical Points:
To determine if the critical point x = 1 is a maximum, minimum, or neither, we can use the second derivative test.
Taking the second derivative of f(x):
f''(x) = -2

Since f''(1) = -2 < 0,="" the="" critical="" point="" x="1" is="" a="" local="" />

Conclusion:
Therefore, the function f(x) = 2x - x^2 - 3 has only a maximum at x = 1.
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The function f(x) = 2x - x2 + 3 hasa)a maxima at x = 1 and a minima atx = 5b)a maxima at x = 1 and a minima at x = -5c)only a maxima at x = 1d)only a minima at x = 1Correct answer is option 'C'. Can you explain this answer?
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