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I have this distance time graph where I need to find the speed after 0s, 2s, 4s. enter image description here

How would I proceed with this? I'm trying to learn derivatives, but I'm stuck here.

ckvywk
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    draw a tangent at each point and measure the gradient – David Quinn Mar 16 '22 at 10:22
  • As you can see I've tried doing it, but I'm not sure how would I be able to draw the 'right' tangent line. How can I get the slope right? – ckvywk Mar 16 '22 at 10:32
  • The speed (the derivative) is the slope of the tangent at the given points. If you need to approximate this graphically, you would draw the tangent first, then make a right triangle with it where you can estimate the slope as $\tan \phi$ of the angle $\phi$ between your tangent and the x axis. – Cristian Gratie Mar 16 '22 at 10:33
  • you can only hope to get a rough estimate of the speed this way since you don't have the formula for the graph – David Quinn Mar 16 '22 at 10:53
  • Ah! Thank you. I've figured it out. – ckvywk Mar 16 '22 at 11:03

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Obviously a graphical construction cannot give an exact result. Anyway, as in the figure, If $A$ is a point of the $x$ axis and $B$ the corresponding point on the graph, take the tangent at $B$ than a point $C$ such that $\overline {CA}=1$, and take the line parallel to the tangent from $C$, That intercepts $AB$ at $D$. $\overline {AD}$ is the value of the derivative of the function at $A$. enter image description here

Emilio Novati
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