Question

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


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Answer 1

Answer:

$f(x) = - {(x - 1)}^{2} + 2$

we have,

$- {(x - 1)}^{2} \leqslant 0 \: for \: all \: x \: e \: r$

$= - {(x - 1)}^{2} + 2 \leqslant 0 \: for \: all \: x \: e \: r$

$f(x) \leqslant 2 \: for \: all \: x \: e \: r$

∴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 2

Answer:

$f(x) = - {(x - 1)}^{2} + 2$

we have,

$- {(x - 1)}^{2} \leqslant 0 \: for \: all \: x \: \: e \: \: r$

$- {(x - 1)}^{2} + 2 \: \leqslant 0 \: for \: all \: x \: e\: r$

$f(x) \leqslant2 \: for \: all \: x \: e \: r$

∴x=2 is the maximum value.

The function doesn't attain the minimum value at any point in its domain.