Question
Local Extrema The graph of a polynomial function is given. From the graph, find (a) the $x$ - and $y$ -intercepts, and (b) the coordinates of all local extrema.$$P(x)=-x^{2}+4 x$$
Step 1
To do this, we set $P(x)$ equal to zero and solve for $x$: $$ 0=-x^{2}+4 x $$ Factoring out an $x$ gives us $x(-x+4)=0$. Setting each factor equal to zero gives us the solutions $x=0$ and $x=4$. These are the $x$-intercepts of the function. Show more…
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