Okay, so I have a calc problem:
Directions say this problem has one local max and one local min point.
f(x)= (-1/3)x³+2x²-12
Math I've done:
d/dx = 3(-1/3)x²+4x
d/dx = -x²+4x
0 = -x²+4x
0/-x = -x²+4x / (-x)
0 = x - 4
so x = 4
then
d²/dx² = -2x+4 | x=4
= -2(4)+4 = -4 < 0
so concave down, with local max @ x=4, and no local min and no inflection point.
BUT if I don't simplify 0 = -x²+4x ... x = 0 or 4. and then:
d²/dx² = -2x+4 | x=0,4
= -2(0)+4 = 4 > 0
= -2(4)+4 = -4 < 0
and then there is a local min @ x=0 and a local max @ x=4
then:
d²/dx² = -2x+4
0 = -2x+4
-4 = -2x.. -4/(-2) = -2x/(-2)
2 = x ... so inflection point at x = 2.
The book has the bottom answer and I'm sure its correct..
All I want to know is: What am I missing? Why do I get the wrong answer? I've divided both sides by (-x), shouldn't it still work?
If the problem were: 0 = 3x²-27 .. I'd divide both sides by 3, and still get the right answer.
Why not when i divide by x?
2006-09-13
08:29:27
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7 answers
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asked by
Sean06
2