Find the critical points

Calculus
Tutor: None Selected Time limit: 1 Day

Consider the function 

f(x)=−2x3+36x2−162x+1. For this function there are three important intervals: (−∞,A][A,B], and [B,∞) where A and  B are the critical points 

Find A:

Find B:

For each of the following intervals, tell whether f(x) is increasing or decreasing. 

Apr 8th, 2015

Without the function I can only guide through how to solve this type of problem.

Critical points exist in polynomial equations only when the derivative (or gradient) equals 0 or when the point on the derivative does not exist.

Assuming the equation is in the form of #x^2+#x+# or in any form with higher exponets, it is solved as such:

Example:  2/3x^3-5.5x^2+12x+10

The derivative is found by separatly in each component of the equation, multiply the coefficient of the variable by the variable's exponet. Then subtract the exponet by one. If the variable has no exponet, the variable becomes x^0=1 and so the coefficient is only used. If there is no variable, that number disappears because it has no effect to that equations rate of change.

The above example becomes: 2x^2-11x+12

You would then reduce this to the roots (2x+3) and (x+4)

The zeroes of these roots are x=-3/2 and x=-4, which are your critical points. These are the two points on the graph where the line changes directions because at one point the rate of change equals 0.

I'm sorry to not be able to answer the rest without the info.


Apr 8th, 2015

If you would like to give me the excluded info here, I'd be happy to show you the answer in detail.

Apr 8th, 2015

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