what is this derivative: absolute value of 2x-1?

Answer 1

People are giving you conflicting information. The answer is 2 when x>0.5 and -2 when x<0.5, but the important part is for you to be able to prove it to yourself. Otherwise, when the test comes along, having just the answer to a different problem won't help. Recognizing that the absolute value will give two answers is the first thing to remember, but it is also key to understand that it will create an reflection point of undefined slope. The best way to understand this is to graph the equation y = abs(2x-1). Simple plotting will show that the slope of the line is -2 until x=0.5, and 2 thereafter. The key to finding this point of reflection is to set the absolute value equal to zero, not x equal to zero.

You should also realize that an equation could have more than one reflection point, as in abs(x^2 - 1), which has no definable slope at x = +/- 1, or abs(sin x), which has infinite slopeless points (one at each multiple of pi). Just remember that every time the equation within the absolute value brackets crosses the x-axis with a non-zero slope, the derivative will be undefined.

Answer 2

you besides mght won't be able to look to locate the pipe key on your keyboard! keep in mind that |x| is defined as being x while x>=0 and as -x while x<=0. So enable's look at while 2x^2 - 7x - 4 is beneficial or damaging. 2x^2 - 7x - 4 is (2x+a million)(x-4), so it extremely is beneficial while the two the two words are beneficial or the two words are damaging. If 2x+a million>0 and x-4>0, then meaning x>-a million/2 and x>4, which simplifies to x>4. If 2x+a million<0 and x-4<0 then meaning x<-a million/2 and x<4, which simplifies to x < -a million/2. Likewise, the function is damaging for values in between -a million/2 and four. so which you will smash up your function into smaller purposes as follows: f(x) = (-a million/2)(2x^2 - 7x - 4) for x<= -a million/2 or x>=4 f(x) = (a million/2)(2x^2 - 7x - 4) for -a million/2 <= x <= 4. Take the derivatives of those one after the different, as though they have been 2 distinctive issues.

Answer 3

is this clac?

if it is then the deriv is 2. just reduce the power of all the variables and constants. 2x becomes 2^1 and 1 becomes 0.

for absolute value 2x-1<0 and 2x+1>0 solve for both and get x=1/2 and x=-1/2

Answer 4

Abs(2x-1) = 2x-1 when 2x-1 not < 0, or when x not < 0.5
Abs(2x-1) = 1-2x when 2x-1 < 0, or when x < 0.5

So, when x not < 0.5, x'= (2x-1)' = 2
when x < 0.5 x'=(1-2x)' = -2

Note that the derivative doesnt exist at x=0.5, because it is -2 approaching from the left, and 2 approaching from the right...

Answer 5

Hey hey dont panic Im in 7th grade I know this stuff okay you have 2 x -1 2x1 is 2 so just put on the negative sign thats -2 the absolute value is the number away from zero how much is added or subtracted from 0 to make that number which in this case is 2

PS: do your self a favor and dont listen to a guy who calls himself zorro

Answer 6

zorro is right and in longer form it is done as such since all inequalities have two solutions:

remember absolute x=

(x) or -(x) which is always be positive


For x>0 dy/dx(2x-1)=2

For x<0 dy/dx(-2x-1)=-2

and since x must always be greater than zero or smaller than zero, it can never actually be 0 due to the absolute value law.

therefore x=0 undefined

Answer 7

2 if x > 0
-2 if x < 0

Undefined if x = 0