The Derivative Graphically

Thomas J. Pfaff ()
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Thomas J. Pfaff: Ithaca College, Department of Mathematics

Chapter Chapter 9 in Applied Calculus with R, 2023, pp 109-133 from Springer

Abstract: Abstract In the previous chapter we estimated the slope of the tangent line at one specific point. We now take a qualitative look at the slopes of tangent lines and sketch the graph of the derivative of a function. Consider figure 9.1 which is the graph of $$f(x)=x^2$$ f ( x ) = x 2 with five tangent lines at the points labeled P1 through P5. The slopes of the tangent lines at P1 and P2 are negative, while the slopes at P4 and P5 are positive. If we were to order the slopes at the points we would have P1

Date: 2023
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DOI: 10.1007/978-3-031-28571-4_9

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