SOLUTION: Hello. Can you please help me? I need to graph the following function, determine the consecutive integer values of X between which each real zero is located, and estimate the x-

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Question 391047: Hello. Can you please help me?
I need to graph the following function, determine the consecutive integer values of X between which each real zero is located, and estimate the x-coordinates at which the relative maxima and minima occur. Can you please help? Thank you!
f(x)= x^3 + 3x^2
Found 2 solutions by solver91311, richard1234:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!




You cannot determine the consecutive integer values of between which each real zero is located because the zeros are all integers in the first place.





Hence, , , or

Relative maximum appears to be at and relative minimum appears to be at

Check:







or



Hence extrema at or

John

My calculator said it, I believe it, that settles it
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Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
No need to "estimate" the extrema, since it is easy to find the exact value. Taking the derivative of f(x) and setting it to 0,

, it follows that x = 0 or x = -2 (either by factoring or quadratic formula). We can check a possible extrema by finding the numerical derivative at points less than and greater than the number. If they have different signs then it is an extrema, if they have the same sign, then the function rises until , then rises again.
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