OpenStudy (precal):

Calculus Question: If I take the derivative of a function, and plot those critical points, do I test a number from each interval into the y' function

5 years ago
OpenStudy (turingtest):

you mean to find increasing/decreasing intervals? yes

5 years ago
OpenStudy (precal):

yes, to find inc and dec

5 years ago
OpenStudy (anonymous):

yes.

5 years ago
OpenStudy (precal):

thanks guys

5 years ago
OpenStudy (anonymous):

well for your info, if you plug values into y'', you will know whether the graph trend is concave upwards or downwards. that will help you in sketching graph too.

5 years ago
OpenStudy (precal):

thanks

5 years ago
OpenStudy (anonymous):

\[ y=4 x^5-45 x^4+180 x^3-310 x^2+240 x\\ y'= 20 x^4-180 x^3+540 x^2-620 x+240=\\ y'=20 (x-4) (x-3) (x-1)^2 \] You should not consider x=1 at all since (x-1)^2 is greater or equal to zero. To study the sign of y' in this case you study the sign of (x-4)(x-3) only.

5 years ago
OpenStudy (precal):

why would we not include x=1, it is a critical number

5 years ago
OpenStudy (precal):

the whole purpose of sign analysis is that we can talk about the graph of the original function without actually graphing it, the days where technology did not exist

5 years ago
OpenStudy (anonymous):

x=1 is a critical point. it may be a max/min point. once you plug into y'' you will know the nature of it.

5 years ago
OpenStudy (anonymous):

At x=1, you cannot have a maximum or a minimum. The derivative has the same sign before 1 and after 1. So it either increasing thru 1 or decreasing thru 1. To have a max say, f has to be increasing before 1 and decreasing after 1.

5 years ago
OpenStudy (anonymous):

x=1 can be an inflection point. Actually it is.

5 years ago
OpenStudy (anonymous):

yea sorry it's not a max/min point. but if i'm nt mistaken it's an inflection point.

5 years ago
OpenStudy (anonymous):

yes the value of y'' changes from - to +.

5 years ago
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