Question

If f is differentiable at x=a, what does f '(a) represent with respect to f(x)?

Answer 1

f'(a)=d/dx*f(x)

Answer 2

what does that mean in words?

the derivitive of a with respect to x is equal to the derivitive of x?

Answer 3

if f is differentiable at x=a, when you plug a to f'(x), your function will be derivable here, too.

Answer 4

what would f '(a) represent on a graph?

Answer 5

the slope of the tangent line at x=a?

Answer 6

if a is constant, in the graph its slope will be zero so it is a straight line

Answer 7

yes, derivative means the slope

Answer 8

ok, thanks!

that makes way more sense!

Answer 9

when you see a derivative or f'(x) or y' or sth, bear in mind that it means tangent line, slope and so on