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

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,

c.

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,

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

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

x^2*(x-8)=0

then we have

x^2 =0

x =0

or

x-8 =0

x=8

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