Question

for the definition of a derivativewhat does the "h" stand for in f(x+h) - f(x)/h ?

Answer 1

Literally, the distance between x and x+h

Answer 2

You can think of it as the horizontal distance between the two points we're computing the average rate of change between.

Answer 3

so for a purely analytical problem if h is not given it is zero?

Answer 4

If the distance between X and X+H are zero, then H must be zero.

Answer 5

Thank you guys.

Answer 6

@mrd7788 \(h\) is only used for the limit in the definition of the derivative:$$\lim_{h\to0}\frac{f(x+h)-f(x)}{h}=\frac{df}{dx}$$

Answer 7

it's just the \[\Delta x\] in the slope equation. however the derivative is defined as a slope of the line tangent to the curve and thus the operational definition:
\[\lim_{\Delta x \rightarrow 0} [\frac{ (\Delta y) }{ (\Delta x) }] = \lim_{h \rightarrow 0} [\frac{ (f(x+h)-f(x)) }{ h }]\]