[Math] Finding the derivative of a point given only a graph

calculus

So we are given a graph with 3 curves that intersects the positive x-axis 4 times.

Graph
Then asked to estimate the values of $f '(1)$, $f '(2)$ and so on until $f ' (5)$.
I'm assuming we are supposed to find the slope of the tangent line at $x=1$, $x=2$ and so on while estimating the y value for an approximate point. But I have no idea how to even begin since we don't have the original function to find the derivative of…

Best Answer

HINTS

  1. Note you have local maximum at $x=1$ and $x=4$, and alocal min around $2.5$. What is $f'$ at those points?
  2. Is $f$ increasing or decreasing on $(1,2.5)$? What is the sign of $f'$ there?
  3. Compare to a line parring roughly through the same points $(1,2)$ and $(2.5, -3)$ - what is the slope of the line, is $f$ increasing or decreasing faster?
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