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# c2 differentiation watch

1. This is the solution to a differentiation question where I have to find the values for x for which f(x) is an increasing function. I would just like to know what is happening on the last two lines. x=1 twice so what do all those symbols mean. My teacher told me to look at the back of the book ; and that was pretty useless for me
2. What that last line

translates to is:

'x' is in the set of real numbers and 'x' is not equal to 1.

f(x) is your function. f'(x) is the derivative of that function. The derivative tells you the functions gradient. So when the derivative is positive, ie f'(x) > 0, that is when the function is increasing. You are looking for all the points where f'(x) > 0.

What you notice in the last line is that you get

.

You know that all squared numbers are positive and so that means . The only time it isn't greater than zero is when x = 1, because that you get , i.e the gradient is 0 (and therefore not increasing).

So your set of values that give f'(x) > 0 are any 'x' values (i.e ) except when x = 1.

Does this make sense?
3. (Original post by claret_n_blue)
What that last line

translates to is:

'x' is in the set of real numbers and 'x' is not equal to 1.

f(x) is your function. f'(x) is the derivative of that function. The derivative tells you the functions gradient. So when the derivative is positive, ie f'(x) > 0, that is when the function is increasing. You are looking for all the points where f'(x) > 0.

What you notice in the last line is that you get

.

You know that all squared numbers are positive and so that means . The only time it isn't greater than zero is when x = 1, because that you get , i.e the gradient is 0 (and therefore not increasing).

So your set of values that give f'(x) > 0 are any 'x' values (i.e ) except when x = 1.

Does this make sense?
Ah I get it perfectly, thanks

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