Q-Find the maximum and the minimum values, if any, without using derivatives of the following functions:
Q-f (x) = –(x – 1)2 + 2 on R
Note_DoNt SpaM
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Q-Find the maximum and the minimum values, if any, without using derivatives of the following functions:
Q-f (x) = –(x – 1)2 + 2 on R
Note_DoNt SpaM
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Answer:
[tex]f(x) = - {(x - 1)}^{2} + 2[/tex]
we have,
[tex] - {(x - 1)}^{2} \leqslant 0 \: for \: all \: x \: e \: r[/tex]
[tex] = - {(x - 1)}^{2} + 2 \leqslant 0 \: for \: all \: x \: e \: r[/tex]
[tex]f(x) \leqslant 2 \: for \: all \: x \: e \: r[/tex]
∴x=2 is the maximum value.
The function doesn't attain the minimum value at any point in its domain.
Step-by-step explanation:
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Answer:
[tex]f(x) = - {(x - 1)}^{2} + 2[/tex]
we have,
[tex] - {(x - 1)}^{2} \leqslant 0 \: for \: all \: x \: \: e \: \: r[/tex]
[tex]- {(x - 1)}^{2} + 2 \: \leqslant 0 \: for \: all \: x \: e\: r[/tex]
[tex]f(x) \leqslant2 \: for \: all \: x \: e \: r[/tex]
∴x=2 is the maximum value.
The function doesn't attain the minimum value at any point in its domain.