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I am a beginner in calculus and I am not exactly sure how to find the derivative of the graph in the diagram. Can someone guide me on how to do this?

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  • $\begingroup$ Can you explain what the symbol $f'(1)$ means, geometrically? $\endgroup$
    – user296602
    Dec 24, 2015 at 1:06
  • $\begingroup$ I am completely new at this so I am not exactly sure. $\endgroup$ Dec 24, 2015 at 1:08
  • $\begingroup$ Well, have you ever seen the symbol $f'(1)$ before? Have you read a definition of it? Do you know the word "derivative"? $\endgroup$
    – user296602
    Dec 24, 2015 at 1:10
  • $\begingroup$ A derivative is basically the instantaneous rate of change (the change at one single point) of a function. $\endgroup$ Dec 24, 2015 at 1:13
  • $\begingroup$ f′(1) is the derivative of the function with an input of 1. $\endgroup$ Dec 24, 2015 at 1:15

1 Answer 1

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The derivative at a point is the slope of the tangent at that point. With this in mind, it is clear that $f'(1) = 0$ and $f'(3) = -1/2$.

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  • $\begingroup$ Ahh okay, so the input (i.e 1 and 3) basically means to find the the slope of the tangent at that point, right? Thanks for the answer. :D $\endgroup$ Dec 24, 2015 at 1:36

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