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Find all critical numbers and use the First Derivative Test to classify each as the location of a location maximum, local minimum, or neither. y = x^4 + 4x^3  2
 one year ago
 one year ago
Find all critical numbers and use the First Derivative Test to classify each as the location of a location maximum, local minimum, or neither. y = x^4 + 4x^3  2
 one year ago
 one year ago

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onegirlBest ResponseYou've already chosen the best response.1
@electrokid can u help?
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
using our previous discussions, you can start the work and I guide.
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
step 1) first derivative \(y'=?\)
 one year ago

onegirlBest ResponseYou've already chosen the best response.1
Sorry i replied late i had internet issues. but the first derivative is 4x^2(x + 3)
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
good. step 2) solve for "x": \(4x^2(x+3)=0\)
 one year ago

onegirlBest ResponseYou've already chosen the best response.1
okay i got x = 3 and x = 0
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
good. those are the critical points. step 3) classify as maxima, minima or neither step 3.1) find second derivative of "f" > find f''(x)
 one year ago

onegirlBest ResponseYou've already chosen the best response.1
are u there @electrokid
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
step 3.1) find the second derivative.
 one year ago

PeterPanBest ResponseYou've already chosen the best response.2
Remember the critical points that you got? If the second derivative is positive when evaluated at one of those critical points, that critical point would be a local minimum. On the flipside, if the second derivative is negative when evaluated at a critical point, that point would be a local maximum.
 one year ago

onegirlBest ResponseYou've already chosen the best response.1
so i substitute those critical point into the second derivative
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
yes. \(f''(x)=12x^2+24x\) step 3.2) plug in x=3 in this equation and check the sign..
 one year ago

onegirlBest ResponseYou've already chosen the best response.1
and when i plugged in 0 i got 0
 one year ago

PeterPanBest ResponseYou've already chosen the best response.2
Okay, so, f''(3) = 36 This is positive, therefore...?
 one year ago

PeterPanBest ResponseYou've already chosen the best response.2
a local minimum ;) What about f''(0) ?
 one year ago

PeterPanBest ResponseYou've already chosen the best response.2
It's neither positive nor negative, right?
 one year ago

PeterPanBest ResponseYou've already chosen the best response.2
Well, what does that mean, then?
 one year ago

PeterPanBest ResponseYou've already chosen the best response.2
It will be neither :D
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
@PeterPan and @onegirl both did a great job and effort and both deserve a medal :) so, @onegirl give one to PPan ☮
 one year ago
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