calculus
posted by Kelly
f'(x) < 0 if x < 1
And apparently this means f is decreasing on (1, 1).
I don't understand this. I know f'(x) < 0 means the function is decreasing. But I don't understand the absolute value. It means I can put 1 or 1 inside, but wouldn't it still be 1 = 1 and not 1 < 1? I don't understand.

bobpursley
Consider f(x)=x^2 1
f(x) <0 if abs(x)<1
However, f(x) is not decreasing over that entire range (1 to 1)
So your meaning of the problem statement is not understood 
Kelly
Sorry, I don't understand your reply...
This question has a prime after the f by the way. It's f prime, aka the derivative. That's why the function is decreasing.
Respond to this Question
Similar Questions

biology
I understand that a prokaryotic cell has ribosomes smaller than 70s. But what i don't understand is what 70s accutually means. Please could someone explain what 70s means to me? 
math
I have the upse question and want to know what the upse stands for. I think the u means understand, p means plan and s means solve and e means evaluate, but I am not sure. I would also like an example of this. 
calculus
is the function f(x)=x^2 increasing on decreasing at x = 1. can anyone please check my reasoning: the value of the derivative of the function at x=1 is 2, so that means the slope of the tangent line to the graph at that is a negative … 
calculus
I don't understand how to do this? I don't know the steps on how to do it! Can you please just tell me the steps? 
Engineering Calculus
f(x)=((6x3)/(x+6)) how do you find the intervals of decreasing and increasing...I found that there were no critical points yet I was also correct that the function increased (I,6) and (6,I). I was wrong that there were no decreasing … 
Calculus
Find the intervals on which the given function is increasing and decreasing. y=x^22x y'=2x2 critical point x=1 Increasing [infinity,1) Decreasing (1,infinity] is this the correct way of writting this wiht the brackets 
Chemistry
In a heating and cooling curve, I understand that the flat part means that the bonds are either forming or breaking, depending on if the input of energy is increasing or decreasing, but what is happening to the bonds in the slanted … 
Calculus
For f(x)=2(x+5)^3 +7 Find and classify the extreme values, determine where the function is increasing and decreasing, where it is concave up and concave down, and any points of inflection. I understand this is using the first and second … 
math
is the statement f(x)= f(x) always true, sometimes true or never true use examples. If f(x) means the function of x then it means the absolute value of the function of x equals the function of the absolute value of x. I do not … 
Calculus
Find the open intervals on which f(x) = 6x^2 + 96x + 7 is increasing or decreasing. a. increasing on (inf, 16); decreasing on (16, inf). b. increasing on (inf, 14); decreasing on (14, inf). c. increasing on (inf, 84); decreasing …