+38 A.) How can I get on which interval is the function increasing and decreasing with using derivation?
y(x)=x^2-ln(x^2)
?
B.)
y(x)=x^2/2*x
y'(x)=1/2 and then i dont know how next :(
THANK YOU GUYS VERY MUCH
+128485 Let's take the second function, first...we have
y(x) = (x^2) / (2x)....if we simplify this "rational function," we get
y(x) = (1/2)x Note that this is just a linear function with a "hole" at x =0 (because we can't divide by zero in the original function)
This function is constantly increasing on the intervals where it is defined (-inf,0) U (0,inf), just as your derivative indicated
As to the first function, I don't know of any way to find the intervals of increase or decrease, except by graphing......here's a graph (I hope it displays correctly)
If we DID take the derivative, we'd find that this function has "minimums" at x = -1 and x = 1.
The intervals of decrease are (-inf, -1) and (0, 1)
The intervals of increase are (-1, 0) and (1, inf)
I think this is correct....maybe some other forum members know a way to find the intervals of increase and decrease with respect to the second function without graphing or calculus......
+128485 Let's take the second function, first...we have
y(x) = (x^2) / (2x)....if we simplify this "rational function," we get
y(x) = (1/2)x Note that this is just a linear function with a "hole" at x =0 (because we can't divide by zero in the original function)
This function is constantly increasing on the intervals where it is defined (-inf,0) U (0,inf), just as your derivative indicated
As to the first function, I don't know of any way to find the intervals of increase or decrease, except by graphing......here's a graph (I hope it displays correctly)
If we DID take the derivative, we'd find that this function has "minimums" at x = -1 and x = 1.
The intervals of decrease are (-inf, -1) and (0, 1)
The intervals of increase are (-1, 0) and (1, inf)
I think this is correct....maybe some other forum members know a way to find the intervals of increase and decrease with respect to the second function without graphing or calculus......
