Polynomial Functions of Higher Degree

label Calculus
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How to A. sketch the graph of the function by applying the leading coefficient test, B.finding the zeros of the polynomial  c. plotting sufficient solution points and d. drawing a continuous curve through the points.

f(x)= 3x^3 - 24x^2

Oct 7th, 2015

Thank you for the opportunity to help you with your question!

A. since the leading coefficient 3>0, the function looks like 3x^3 as x goes to -infinity and infinity. 

B. 3x^3-24x^2 = 3x^2(x-8)

zero is x = 0 or x = 8, 


since x =0 has x^2, the function >0 near x =0, 

d. x <8 f(x)<0, and f(x)>0 for x>0, 

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 7th, 2015

Thanks! Can you show me the steps for finding the zeroes?

Oct 7th, 2015

just let  3x^3-24x^2 = 3x^2(x-8)=0, so we have 


then we have 

x^2 =0 

x =0 


x-8 =0  


Oct 8th, 2015

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