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# c2 differentiation symbols? watch

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1. ex 9A que 1f

find values of x for which f(x) increases,
f(x)=5x^3 + 12x
f'(x)=15x^2 + 12
so f'(x)>0
=> 15x^2 + 12 > 0

this is where my answer stops, i would think no solutions for x; but the answer at the back is x ∈ ℝ, what do these symbols mean???
2. Cant view what the symbols are...is it x e R?
3. x E R means that "x is any real number" i.e. that x^2 + 12 > 0 for any number that you can name, be it negative, a fraction, or something like root 2 or pi which are irrational numbers.

x^2 + 12 - well, x^2 will always be greater than or equal to zero (if you square a number then you always get a positive number, the smallest possible number you can get is 0). then if you add 12 to that you will always get a number that is bigger than 0 (you'll always get a result that is bigger than or equal to 12).
There are weird things involving the square roots of negative numbers, which are not called real numbers, and that's where the "x E R" bit comes from.

love danniella
4. Or more simply you rearrange to get x2>-4/5 which you know is always true for all values of x on the Real number line.

Out of interested, how did you get that ℝ symbol? It doesn't appear to be in charmap and Opera (my browser) normally dislikes non-standard characters.
5. (Original post by danniella)
x E R means that "x is any real number" i.e. that x^2 + 12 > 0 for any number that you can name, be it negative, a fraction, or something like root 2 or pi which are irrational numbers.

x^2 + 12 - well, x^2 will always be greater than or equal to zero (if you square a number then you always get a positive number, the smallest possible number you can get is 0). then if you add 12 to that you will always get a number that is bigger than 0 (you'll always get a result that is bigger than or equal to 12).
There are weird things involving the square roots of negative numbers, which are not called real numbers, and that's where the "x E R" bit comes from.

love danniella
that's what i wanted, thank you
6. (Original post by AlphaNumeric)
Or more simply you rearrange to get x2>-4/5 which you know is always true for all values of x on the Real number line.

Out of interested, how did you get that ℝ symbol? It doesn't appear to be in charmap and Opera (my browser) normally dislikes non-standard characters.
copied right out of c2 solutionbank. thanks for the simple alternative!

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