Finding Velocity Zero: Solving a High School Calculus Problem

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[SOLVED] high school calc problem

Homework Statement


If an object moves along the y-axis (marked in feet) so that its position at time x (in seconds) is given by the indicated function; y= (x^3)-(9x^2)+15x;
Find when v=0


Homework Equations


v=y prime, and i already have found y prime to be (3x^2)-(18x)+15


The Attempt at a Solution


I checked the selected answers in the back of the book and did a little plug and chug and called it a day...:blushing:.. haha. I'm assuming there's a more relevant process so any help is mucho appreciated. thanks.
 
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if v=y'

then shouldn't v=3x^2-18x+15

when v=0

3x^2-18x+15=0


try some factorisation
 
wow...thank you

haha I am not sure how i didn't see that. I really didn't think anyone would answer. I believe I've just found a new home for homework help...and considering I will be going into chemE next next year in college, I should be revisiting many of times!

haha thank you a lot!
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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