Is $f(x)=(x-3)/sqrt(x+3)$ increasing or decreasing at $x=3$ ?

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Is $f(x)=(x-3)/sqrt(x+3)$ increasing or decreasing at $x=3$ ?

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Answer 1 · 2016-11-24T21:55:15

You have to look at the sign of the derivative of the function for $x=3$

Explanation:

$f(x) = (x-3)/sqrt(x+3) = (x-3)(x+3)^(-1/2)$

$(df)/(dx) = (x+3)^(-1/2) -1/2 (x-3)(x+3)^(-3/2)$

$(df)/(dx) |_(x=3) = 1/sqrt(6) > 0$

So the function is increasing.

On the other hand it is easy to see that $x=3$ is a zero of $f(x)$ and as the denominator is always positive and the numerator is negative for $x<3$ and positive for $x>3$ the function must be increasing.

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Is $f(x)=(x-3)/sqrt(x+3)$ increasing or decreasing at $x=3$ ?

1 Answer

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Is f(x)=(x-3)/sqrt(x+3) f(x)=(x-3)/sqrt(x+3) increasing or decreasing at x=3 x=3 ?

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Explanation:

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Is $f(x)=(x-3)/sqrt(x+3)$ increasing or decreasing at $x=3$ ?