Question

What does "symmetry" mean in calc?

Answer 1

That there is a mirrorplane/point/line...
The equation is similarly shaped on both sides of this mirror

Answer 2

but they use it like "Deduce the value of f'(1) f'(2) using symmetry." and give you a graph of

Answer 3

1 sec let me get the graph

Answer 4

f(x) = x^2

Answer 5

symmetry axis = x=0

f`(1) = -f`(-1)
f'(2) =-f'(-2)

Does that help?

Answer 6

so is it just flipping the graph?

Answer 7

More or less. yep

Answer 8

but how would flipping a graph give you a value?

Answer 9

Because the value of the point f'(1) has a relation to the point f'(-1)..

Answer 10

Though you need to know the value of f'(x) in point -1

Answer 11

so would you just add a negative sign in front of it cause it is flipped?

Answer 12

yes, that is what a mirrorplane does.

Answer 13

srry, mirrorline in 2D ;P

Answer 14

cause in my teachers book, it says "f'(-x) = -f'(x)"

Answer 15

Yes, that's what I said, right?

Answer 16

ya.. so is it that simple, just a negative sign?

Answer 17

indeed

Answer 18

ok, thanks