Question

When does the relative max occur
y= -x^3+ 3x^2-2 @Calculus1

Answer 1

please need help!

Answer 2

\[y=-x^3+3x^2-2\]\[y'=-3x^2+6x\]\[y''=-6x+6\]at the max, y'=0 and y''<0,so we get:\[y'=0=-3x^2+6x=3x(-x+2)\]so x=0 or 2. now test what y'' is at each of these values:\[y''(0)=-6*0+6=6\]\[y''(2)=-6*2+6=-12+6=-6\]so max must be at x=2. now work out what y is at x=2:\[y=-(2^3)+3*(2^2)-2=-8+12-2=2\]so we have a max at (2, 2).