Question

Calculus: Is it possible to find the graph of the original function given the graph of its derivative and several points to help set its position? If so, how?

Note: I'm looking for a way to solve this visually(no math). For example, would tangents work?

Answer 1

i know it is possible ...bec there was a question on a test and final exam lol
got it wrong both times :P

Answer 2

I guess by using the fact
if \[\rm f'(x) >0 , then ~f(x) ~is~ increasing \]if\[\rm f'(x) <0 , then ~f(x) ~is~ decreasing\]

Answer 3

yeap as @Nnesha said
check the derivative Extremas and where they occur, for the stationary points and where's undefined, thus all critical points
and check whether the derivative is increasing or decreasing before and after those critical points

then use the original function, to the y-value for that x-value and you can more or less get the original graph

Answer 4

Is that the only way? Can I find the graph by using just tangents?

Answer 5

hmmm no the derivative's Extremas, but the critical points from the derivative to get the original function's Extremas =)

Answer 6

well, Extramas ARE when the slope is 0, or the derivative is 0, thus a horizontal line, thus a "rise" of 0, thus a tangent line in the original function

Answer 7

Ok, thank you :)

Answer 8

yw