Question

Find the (a) the local extrema, (b) the intervals on which the function is increasing, (c) the interval on which the function is decreasing

h(x)=2/x

Answer 1

h'(x) = -2/x^2

a function is increasing when its first derivative is positive, and

a function is decreasing when its first derivative is negative.

now look at our derivative, notice the bottom is a square of x, so no matter what you put in, the result will be positive, and this is divided into -2.

so what result will we get??

also notice that both the original and the derivative are undefined for x=0