Sketch the graph by hand using asymptotes and intercepts, but not derivatives. Then use your sketch as a guide to producing grap

Question

2 years ago

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Sketch the graph by hand using asymptotes and intercepts, but not derivatives. Then use your sketch as a guide to producing grap

hs (with a graphing device) that display the major features of the curve. Use these graphs to estimate the maximum and minimum values. (Round your answers to three decimal places.)
f(x) = (2x+3)²(x-2)^5/x³(x-5)²

Mathematics

1 answer:

Arisa [49] · Answer 1 · 2023-08-26T23:38:43+03:00

The local minima of $f\left(x\right)=\ \frac{\left(2x+3\right)^2\left(x\ -2\right)^5}{x^3\left(x-5\right)^2}$ are (x, f(x)) = (-1.5, 0) and (7.980, 609.174)

<h3>How to determine the local minima?</h3>

The function is given as:

$f\left(x\right)=\ \frac{\left(2x+3\right)^2\left(x\ -2\right)^5}{x^3\left(x-5\right)^2}$

See attachment for the graph of the function f(x)

From the attached graph, we have the following minima:

Minimum = (-1.5, 0)

Minimum = (7.980, 609.174)

The above means that, the local minima are

(x, f(x)) = (-1.5, 0) and (7.980, 609.174)