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What is the maximum value of the function f(x) = 2x2 - 2x + 6 in the interval [0, 2]?
- a)6
- b)10
- c)12
- d)5.5
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
What is the maximum value of the function f(x) = 2x2 - 2x + 6 in the i...
We need absolute maximum of
f(x) = 2x2 - 2x + 6
in the interval [0, 2]
First find local maximum if any by putting f'{x) = 0
is a point of local minimum. So there is no point of local maximum.
Now tabulate the values of f at end point of interval and at local maximum if any (in this case no point of local maximum).
Clearly the absolute maxima is at x = 2 and absolute maximum value is 10.
f(x) = 2x2 - 2x + 6
in the interval [0, 2]
First find local maximum if any by putting f'{x) = 0
is a point of local minimum. So there is no point of local maximum.
Now tabulate the values of f at end point of interval and at local maximum if any (in this case no point of local maximum).
Clearly the absolute maxima is at x = 2 and absolute maximum value is 10.
Most Upvoted Answer
What is the maximum value of the function f(x) = 2x2 - 2x + 6 in the i...
Solution:
To find the maximum value of the function f(x) = 2x^2 - 2x + 6 in the interval [0, 2], we need to follow the following steps:
Step 1: Find the derivative of the function f(x) with respect to x.
f'(x) = 4x - 2
Step 2: Find the critical points of the function f(x) by setting f'(x) = 0.
4x - 2 = 0
x = 0.5
Step 3: Check the nature of the critical point by using the second derivative test.
f''(x) = 4 > 0
Since f''(x) is positive, the critical point x = 0.5 is a point of minimum.
Step 4: Evaluate the function at the endpoints of the interval [0, 2].
f(0) = 6
f(2) = 14
Step 5: Compare the values obtained in Step 3 and Step 4 to find the maximum value of the function in the interval.
Maximum value of the function f(x) = 2x^2 - 2x + 6 in the interval [0, 2] is 10, which is obtained when x = 1.
Therefore, the correct answer is option B) 10.
To find the maximum value of the function f(x) = 2x^2 - 2x + 6 in the interval [0, 2], we need to follow the following steps:
Step 1: Find the derivative of the function f(x) with respect to x.
f'(x) = 4x - 2
Step 2: Find the critical points of the function f(x) by setting f'(x) = 0.
4x - 2 = 0
x = 0.5
Step 3: Check the nature of the critical point by using the second derivative test.
f''(x) = 4 > 0
Since f''(x) is positive, the critical point x = 0.5 is a point of minimum.
Step 4: Evaluate the function at the endpoints of the interval [0, 2].
f(0) = 6
f(2) = 14
Step 5: Compare the values obtained in Step 3 and Step 4 to find the maximum value of the function in the interval.
Maximum value of the function f(x) = 2x^2 - 2x + 6 in the interval [0, 2] is 10, which is obtained when x = 1.
Therefore, the correct answer is option B) 10.
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