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Question
If x is real, the minimum value of x2 – 8x + 17 is ______.
Options
– 1
0
1
2
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Solution
If x is real, the minimum value of x2 – 8x + 17 is 1.
Explanation:
Let f(x) = x2 – 8x + 17
f'(x) = 2x – 8
For local maxima and local minima, f'(x) = 0
∴ 2x – 8 = 0
⇒ x = 4
So, x = 4 is the point of local maxima and local minima.
f'(x) = 2 > 0 minima at x = 4
∴ `"f"(x)_(x = 4)` = = (4)2 – 8(4) + 17
= 16 – 32 + 17
= 33 – 32
= 1
So the minimum value of the function is 1.
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