Find the intervals of increase/decrease of this function?

Question

The function is abs(x^2-6x+5) ((absolute value of it))
the zeros are x=5,1.
i took the two equations (since it is greater than or equal to zero and less than zero, ((negatedthe part less than zero, and then took the first derivative))
but i got the critical points to be 3, when on the graph it doesnt go through 3.
any help on what to do? thanks.

yes, but how do i determine the intervals of increase/decrease with this function?

Answer 1

Hi, I just bumped into another of your questions.
When solving these type of questions it is useful to draw the, in this case, parabola, without the absolute value.
Because of the absolute value, everything will be positive. So if you could do the symetric around the x-axis of the negative part you will obtain the abs(fx).

To answer your question, the function will drop towards the x axis from (-oo,+oo) to x=1 where it will be zero. Then it will go up, like a normal parabola with a maximum at x=3 (y = 4). Then it will go down until it reaches x=5 (y=0) and will start growing again.

If you want to see the shape fast, take some transparent paper, draw a parabola like an inverted U and then fold the paper by the middle (this will be your x-axis) and look at the figure against a light source. The graph will resemble a w.

Hope this helps. Best?

Answer 2

The critical point is 3. The graph goes through the point (3,4), which is a local maximum for the function.

Answer 3

after u graph the two equations, it will be simpler to solve. you will see the first interval it wil decrease from (infiniti,1] infiniti until 1, then increases from [1,3] then decrease form [3,5] then increase from [5,infiniti] the number sare vallues of x.

Answer 4

it may rely what point math you're at. In calculus you will discover the 1st derivative and spot the place it relatively is effective (increasing) or damaging (reducing). In algebra you ought to graph them.