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=

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) (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.
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