Let f - R - R be the function f x - x- a 1 x- a 2 - x- a 2 x- a 3 - x- a 3 x- a 1 with a 1 - a 2 - a 3 - R- Then f x - 0 if and only if

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First Derivative Test for Local Maximum

Let f : R →...

Question

Let $f : R \to R$ be the function $f (x) = (x - a_{1}) (x - a_{2}) + (x - a_{2}) (x - a_{3}) + (x - a_{3}) (x - a_{1})$ with $a_{1}, a_{2}, a_{3} \in R$ . Then $f (x) \geq 0$ if and only if

At least two of

a_{1}, a_{2}, a_{3}

are equal

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a_{1} = a_{2} = a_{3}

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a_{1}, a_{2}, a_{3}

are all distinct

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a_{1}, a_{2}, a_{3}

are all positive and distinct

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Solution

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Similar questions

f : R \to R

f (x) = (x - a_{1}) (x - a_{2}) + (x - a_{2}) (x - a_{3}) + (x - x_{3}) (x - x_{1})

a_{1}, a_{2}, a_{3} \in R

\geq 0

a_{1}, a_{2}, a_{3}, . . . a_{n}

\frac{a_{1}}{a_{2} + a_{3} + . . . a_{n}}, \frac{a_{2}}{a_{1} + a_{3} + . . . a_{n}}, \frac{a_{3}}{a_{1} + a_{2} + a_{4} + . . . + a_{n}}, \frac{a_{n}}{a_{1} + a_{2} + . . . + a_{n}}

If A₁, A₂, A₃,..., A_n are n numbers between a and b, such that a, A₁, A₂, A₃,..., A_n, b are in A.P., then

a_{1}, a_{2}, a_{3}, . . . . a_{n}

\frac{a_{1}}{a_{2} + a_{3} + . . . . + a_{n}}, \frac{a_{2}}{a_{1} + a_{3} + . . . . + a_{n}}, . . . ., \frac{a_{n}}{a_{1} + a_{2} + . . . . + a_{n - 1}}

a_{1}, a_{2}, a_{3}, . . . . . a_{n}

\frac{a_{1}}{a_{2} + a_{3} + . . . a_{n}}, \frac{a_{2}}{a_{1} + a_{3} + . . . . + a_{n}}, \frac{a_{n}}{a_{1} + a_{2} + . . . + a_{n - 1}}

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