SOLUTION: Graph the function f(x)=x^3-2x^2+x by finding its zeros. Use the graph to estimate where the instantaneous rate of change is positive, negative, and zero.
Thanks
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Question 1153827: Graph the function f(x)=x^3-2x^2+x by finding its zeros. Use the graph to estimate where the instantaneous rate of change is positive, negative, and zero.
Thanks
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Zeros at x for -1, 0, and 1.
You could estimate the rate of change information by examining the graph.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
Note the factorization and the graph shown in the response from the other tutor are fine; but they have listed the roots incorrectly.
There is a single root at x=0 and a double root at x=1; the graph shows that clearly.
For finding where the instantaneous rate of change is positive, negative, or zero, we can first tell that the rate is 0 at exactly x=1 because of the double root. And the graph shows that the rate of change is positive for x > 1 and negative just to the left of x=1.
The graph clearly shows that the rate of change is also zero somewhere between 0 and 1. Since the instructions are to estimate, it looks like the rate is 0 at about x = 1/3. (And calculus would tell us that is exactly right....)
And the rate of change is clearly positive to the left of that point, and negative between that point and x=1.
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