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...
- Calculus - Find the absolute maximum and absolute minimum values of the function...
- Calculus - Find the Absolute Maximum and Absolute Minimum of f on (0,3]. f(x)=(x...
- calculus - 2) Let g(s)= t(4−t)^1/2 on the interval [0,2]. Find the ...
- calculus - Let M=1000. Which of the conditions is equivalent to f(x)= 1/((4x-12...
- Calculus - Find the absolute extrema of the function on the interval [2, 9]. (...
- Calculus - Consider the function f(x) = x^4 - 72 x^2 + 3, -5 less than or equal...
- calculus - Consider the function f(x)=(x^3)(e^9x), -2 is less than or equal to x...
- Calculus - Find the absolute extrema of the function. (Round your answer to ...

More Related Questions