Homework Help: Pre-Calculus

Posted by Stacy on Saturday, November 19, 2011 at 2:28pm.

I'm having problems solving this and showing the steps:

Find the absolute maximum and absolute minimum, if either exists, for

y = f(x)= x^3 - 12x + 12 -3 less equal to x greater than equal to 5

Pre-Calculus - Stacy, Saturday, November 19, 2011 at 2:59pm
I'll rewrite the equation.
y = f(x) = x^3 -12x + 12
-3 <= x >= 5
Pre-Calculus - Damon, Saturday, November 19, 2011 at 3:33pm
dy/dx = 3x^2 -12
function is horizontal when dy/dx = 0
that is when
x^2 = 4
x = +/- 2
when x = -2
f(-2) = -8 + 24 + 12 = 28
and
d^2y/dx^2 = 6 x = -12 so a maximum
when x = 2
f(2) = -4
and
d^2y/dx^2 = 6x = +12 so a minimum
now check the end points
when x = -3
f(-3) = -27+36+12 = 21
when x=+5
f(5) = 125 - 60 +12 = 77
so the maximum is 77 at x = 5
and the minimum is -4 at x = 2
Pre-Calculus - Stacy, Saturday, November 19, 2011 at 3:55pm
Thank you so much. This is a great help. I can see where I started to go wrong.

Answer this Question

Related Questions

Calculus (pleas help!!!) - Find the absolute maximum and absolute minimum ...
Calculus (pleas help!!!) - Find the absolute maximum and absolute minimum values...
absolute maximum - absolute maximum of (x^2-4)/(x^2+4) the critical numbers i ...
Calculus - Find the absolute maximum and absolute minimum values of f(x)=sinx...
Calculus - Determine where the absolute extrema of f(x)=-3(x^2)+7x on the ...
calculus - Find the absolute maximum and absolute minimum values of f on the ...
Calculus - Find any absolute maximum and minimum and local maximum and minimum ...
Calculus - Find the absolute maximum value and the absolute minimum value, if ...
Math I'm so confused - Find the absolute maximum and absolute minimum values...
calculus - Find the absolute maximum and absolute minimum values of f on the ...

For Further Reading

First Name:
School Subject:
Answer: