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Forums
Mathematics
Calculus
Determine the relative maximum and minimum on the graph
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[QUOTE="I like Serena, post: 6782080, member: 312166"] Let's add the graph of $\color{red}f(x)$ at an arbitrary level. That is, let's pick $\color{red}f(0)=0$. And let's assume that $\color{red}f(x)$ is continuous at $x=10$. \begin{tikzpicture}[ declare function={ df1(\x) = 2*cos(3/11*360)-2*cos((\x+1)/11*360); df2(\x) = 1.25-5/16*(\x-13)^2; f1(\x) = 2*cos(3/11*360)*\x-2*(sin((\x+1)/11*360) - sin(1/11*360))*11/(2*pi); f2(\x) = 1.25*(\x-10)-5/16*((\x-13)^3 + 27)/3+f1(10); }] %\draw[help lines] (-1,-3) grid (16,4); \draw[-latex] (-1,0) -- (16,0); \draw[-latex] (0,-3) -- (0,4); \draw foreach \i in {1,...,15} { (\i,0.1) -- (\i,-0.1) node[below] {$\i$} }; % \draw foreach \i in {-2,...,2} { (0.1,\i) -- (-0.1,\i) node[ left ] {$\i$} }; \draw[domain=-1:10, variable=\x, thick, smooth] plot ({\x}, {df1(\x)}) (3, {df1(3)}) node[above left] {$f'(x)$}; \draw[domain=10:16, variable=\x, thick, smooth] plot ({\x}, {df2(\x)}); \filldraw[fill=black!5, thick] (10,{df1(10)}) circle (0.05) (10,{df2(10)}) circle (0.05); \draw[domain=-1:10, variable=\x, red, thick, smooth] plot ({\x}, {f1(\x)}) (9, {f1(9)}) node[above right] {$f(x)$};; \draw[domain=10:16, variable=\x, red, thick, smooth] plot ({\x}, {f2(\x)}); \end{tikzpicture} Can we find those points and intervals now? [/QUOTE]
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Mathematics
Calculus
Determine the relative maximum and minimum on the graph
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