# Is #f(x)=sqrt(1/x-2) # increasing or decreasing at #x=2 /9 #?

##### 1 Answer

Look at the function or take the derivative to find that

#### Explanation:

If we think about what

Then, as

So we know the answer without doing any calculus, but let's do it the calculus way as well. A function is increasing or decreasing at a certain point if its first derivative is positive or negative, respectively. Then, to confirm our answer of decreasing, the first derivative should be negative at

Applying the power rule, the chain rule, and the quotient rule gives us

As the denominator is always positive, then we have