Use a graphing calculator to find the coordinates of the turning ...

Question

Use a graphing calculator to find the coordinates of the turning points of the graph of each polynomial function in the given domain interval. Give answers to the nearest hundredth. ƒ(x)=x^3+4x^2-8x-8; [-3.8, -3]

Accepted Answer

For the following polynomial function with the specified domain, determine the coordinate of the turning point with the help of a graphic utility round your answer to the nearest hundreds. Our function is X to third plus two, X squared minus 11 X minus five all over the domain, negative 3.4 to negative two. We have four possible answers here which are all points. Now to determine this, I first graphed out what our function looks like. It tells us to use a graphing utility. So you can plug this into a graphing calculator and get this graph out. I've graphed it here just so we can see what it looks like. It also tells us the domain we're looking for is over negative 3.4 to negative two. I'll go ahead and mark that on our graph with the red line 83.4. Roughly about here on our graph. We also won the mark negative two, which would be along the vertical line X equals negative two. So we need to find a turning point between those two lines. I'll actually solidify them so I can see them a little better. Now, a turning point on the graph is where our graph changes direction. In other words, if we look between these two lines, we see our graph goes up increases and then at some point it turns the other direction and decreases. This happens at the point negative 2. 19.6. That is over our domain, which means the answer to our problem turns out to be answer c our graphic calculator should be able to tell us where that point is exactly. Ok. I hope to help you solve the problem. Thank you for watching. Goodbye.

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Use a graphing calculator to find the coordinates of the turning points of the graph of each polynomial function in the given domain interval. Give answers to the nearest hundredth. ƒ(x)=x^3+4x^2-8x-8; [-3.8, -3]