Calculus problem, please help?
g(x)= x^3+6x^2+15
Find the largest open intervals where the function is increasing and decreasing.
THE ANSWERS ARE
(-INFINITY,-4);(0,INFINITY) INC.
AND
(-4,0) DEC.
But how did she get those answers??
Update:Imerson, when you did the derivative you just did the math wrong. Its 3x^2+12x.. and then the procedure you did will end up with the answer I had. But since you put your prodedure on there it taught me how to do it, so thank u sooooo much!!!
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That doesn't sound right, should be (-inf , -2), not (-inf , -4)
Are you sure that's the answer?
Here is my procedure, I could be wrong but we just did this in class:
Derive the function -> 3x^2 + 6x
Factor and set equal to zero.
3x(x+2) = 0
x = 0 , x = -2
Draw a little number line, marking 0 and -2
Plug in values from each section of the number line (left of -2, between 0 and -2, and higher than 0) - plug them into the factored thing 3x(x+2)
So for left of -2, you could plug in -3 -> 3(-3)(-3+2) = 9
The value is positive, so the function increases from -infinity to -2
Do the same thing for a value between -2 and zero. Try -1.
3(-1)(-1+2) = -3
The value is negative, so the function decreases from -2 to 0.
And last, plug in a value higher than zero. Let's do 1.
3(1)(1+2) = 9
The value is positive, so the function increases from 0 to infinity.
so increasing from (-inf , -2)U(0 , inf)
decreasing from (-2,0)