Question

Find the values of x for which the function f(x)=x²-2x+1 is increasing or decreasing.Sketch the graph of y=f(x) ?

Answer 1

`y=f(x)=x^2-2x+1` is increasing in the interval `(1,oo)` and it is decreasing in the interval `(-oo,1)`.

Explanation:

A function `y=f(x)` is increasing in the interval where `(dy)/(dx)>0` and is decreasing in the interval where `(dy)/(dx)<0`,

Here `y=x^2-2x+1`

hence `(dy)/(dx)=2x-2`

Now `2x-2>0` means `x>1`, hence `y=x^2-2x+1` is increasing in the interval `(1,oo)`

and `2x-2<0` means `x<1`, hence `y=x^2-2x+1` is decreasing in the interval `(-oo,1)`

graph{x^2-2x+1 [-10, 10, -5, 5]}