The minimum value of fx-aax-a1-ax- where a- x- and a-0- is equal to-

Using AM ≥ GM inequality, we get a^a^x+aa^a^x2≥ ( a^a^x·aa^a^x )^12 ⇒ a^a^x+ a^1 a^x≥2√(a) ...

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Test for Monotonicity about a Point

The minimum v...

Question

The minimum value of $f (x) = a^{a^{x}} + a^{1 - a^{x}}$ , where $a, x \in R$ and $a > 0$ , is equal to:

a + \frac{1}{a}

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a + 1

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2 a

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2 \sqrt{a}

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Solution

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Similar questions

f (x) = a^{a^{x}} + a^{1 - a^{x}}

a, x \in R

a > 0

A = {(x, y) \in R \times R | 2 x^{2} + 2 y^{2} - 2 x - 2 y = 1},

B = {(x, y) \in R \times R | 4 x^{2} + 4 y^{2} - 16 y + 7 = 0}

C = {(x, y) \in R \times R | x^{2} + y^{2} - 4 x - 2 y + 5 \leq r^{2}}

| r |

A \cup B \subseteq C

f (x) = e^{a x} + e^{b x},

a \neq b

f^{''} (x) - 2 f^{'} (x) - 15 f (x) = 0

x \in R

a b

f : R \to R

f (x) = {\begin{matrix} [x], x \leq 2 0, x > 2 \end{matrix},

[x]

x .

I = 2 \int - 1 \frac{x f (x^{2})}{2 + f (x + 1)} d x,

(4 I - 1)

a x + \frac{b}{x}

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