greatest value

**mark** · September 3rd 2009, 04:13 AM

i've been asked to find the greatest value of $\frac {1}{x}$ from $3(x + 2)^2 + 5$ the answer is 1/5 but i was wondering if someone could show me how they would come to that answer, thanks

ps there is supposed to be a function symbol (f) in front of the x but i don't know how to write it out

**red_dog** · September 3rd 2009, 06:59 AM

Do you mean to find the maximum of $\frac{1}{f(x)}$ if $f(x)=3(x+2)^2+5$ ?

**mark** · September 3rd 2009, 07:25 AM

yeah thats the one

**mathaddict** · September 3rd 2009, 07:30 AM

Originally Posted by mark

i've been asked to find the greatest value of $\frac {1}{x}$ from $3(x + 2)^2 + 5$ the answer is 1/5 but i was wondering if someone could show me how they would come to that answer, thanks

ps there is supposed to be a function symbol (f) in front of the x but i don't know how to write it out

1/f(x) is maximum when f(x) is minimum . The minimum of f(x) is 5 so the answer is correct .

**red_dog** · September 3rd 2009, 07:31 AM

In this case the maximum of $\frac{1}{f(x)}$ is reached when $f(x)$ is minimum. The minimum of $f(x)$ is 5, when $x=-2$ .

Then the maximum of $\frac{1}{f(x)}$ is $\frac{1}{5}$ .

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