when i have something like: f(x) = |x^2-x| what does it mean?
Stacey Warren - Expert brainly.com
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this is the absolute value symbol. What does the directions ask of you?
it means that the y value of the ordered pair is x^2-x and that the answer will be 0 or positive.
well it's asking me to find the derivative of that function above. so i'm think there are more than 1 derivatives to find. for instance derivative of f(x) when x >= 0 an derivative when x <0 but i'm not so sure
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you could write it as
for x≥ 1 f(x)= x^2-x
for 0≤x ≤1 f(x)= x-x^2
for x ≤ 0 f(x)= x^2+x
if I did that correctly...
for x <0 x^2-x is much better
Remember, the definition of |x| is:
|x| = x, if x >= 0
|x| = -x, if x < 0.
So: f(x) = |x^2-x| means:
f(x)= x² - x, if x² - x >= 0
f(x)= -x² + x, if x² - x <0
So, to know which of the two formulas applies for certain values of x, you will have to solve x² - x = 0.
It has two (simple to find) solutions. Put them on a number line and then make a sign scheme of x² - x. Then you know which of the two formulas applies where...
well i have this: http://www.sosmath.com/calculus/diff/der13/img5.gif which i don't understand at all! how the get the if's and how they change the signs.
if x > 1 then x^2 is bigger than x and x^2-x is positive | positive #| is just the #
if x between 0 and 1 x^2 is less than x and x^2 -x is negative
the absolute value operation changes this to positive: you could say it multiplies by -1:
The sign scheme is (see image).
So for 0 < x < 1 you have:
f(x) = -(x² - x) = -x² + x (because x²-x is negative there)
for x <=0 and for x >=1 you have:
f(x) = x² - x (because x² - x is positive there, so you just remove the |..| )