SOLUTION: Determine the abscissae of the maxima, minima and inflection points. y = x^4 + 6x^3 - 5 The answer is supposed to be: Minimum at x point = -9/2, inflection points at x=0 and x=

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Determine the abscissae of the maxima, minima and inflection points. y = x^4 + 6x^3 - 5 The answer is supposed to be: Minimum at x point = -9/2, inflection points at x=0 and x=      Log On


   

Question 556891: Determine the abscissae of the maxima, minima and inflection points.
y = x^4 + 6x^3 - 5
The answer is supposed to be: Minimum at x point = -9/2, inflection points at x=0 and x=-3
I don't know how to do this, help me please.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Take the first derivative and set it equal to zero:



This equals zero at x = 0 and x = -9/2. Now take the second derivative and set it to zero to find possible inflection points:



x = 0 and x = -3 are the x-coordinates for possible inflection points. Note that you still have to test these points for concavity, as the concavity does not always change when the second derivative equals zero.