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2019-09-21 14:38:38 +0100 commented question How to plot multiple tangent lines on a graph

I am a Quantitative Epidemiology PhD student brushing up on my calculus skills using a free textbook online called Multivariate analysis.

2019-09-20 23:51:35 +0100 asked a question How to plot multiple tangent lines on a graph

I installed Sage today, so I am unfamiliar with the software. I have an equation f(x)=sqrt(625-x^2), and f'(x)=-x/sqrt(625-x^2). I am trying to plot both f(x) and f'(x) at 20, 24, -7 and -15 on one graph. To begin I tried:

plot(sqrt(625-x^2) + plot(-x/sqrt(625-^2))

This produced:

alt text

Please let me know if the image doesn't appear as this is my first question. Essentially it is a straight line at the intercepts of 25 and 0 on the y axis. How would I create a simple graph that demonstrates f(x) and f'(x) tangent lines at x = 20, 24, -7 and -15? Many thanks.