1. ## greatest value

i've been asked to find the greatest value of $\displaystyle \frac {1}{x}$ from $\displaystyle 3(x + 2)^2 + 5$ 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

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

3. yeah thats the one

4. Originally Posted by mark
i've been asked to find the greatest value of $\displaystyle \frac {1}{x}$ from $\displaystyle 3(x + 2)^2 + 5$ 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 .

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

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