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Question

# Use a graphing calculator or a CAS to plot the graph of each of the following functions on [-1,7]. Determine the coordinates of any global extrema and any inflection points. You should be able to give answers that are accurate to at least one decimal place. (a) $f(x)=x \sqrt{x^2-6 x+40}$ (b) $f(x)=\sqrt{|x|}\left(x^2-6 x+40\right)$ (c) $f(x)=\sqrt{x^2-6 x+40} /(x-2)$ (d) $f(x)=\sin \left[\left(x^2-6 x+40\right) / 6\right]$

Solution

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Step 1
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(a)

$\text{Since, the function is increasing, thus the maxima in the interval } [-1,7] \text{ is } f(7)\approx 47.99.$

$\text{The minima is } f(-1)\approx -6.86, \text{ and the inflection point is } (2.03, 11.47).$

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