Sunday

August 30, 2015
Posted by **Salman** on Sunday, November 22, 2009 at 9:22am.

To find the minimum value of we need to check the value at the following three points (in increasing order). (You will need to use a numerical method, like Newton-Raphson to find one of these points.)

x1=? x2=? x3=?

- Calculus -
**MathMate**, Sunday, November 22, 2009 at 9:54amTo find the minimum of the function, you need to find the derivative, f'(x). At the local minimums, the derivative equals zero. That gives you two of the three points, and for which you can solve using the quadratic formula.

Since the function is not a polynomial (because of the square-root function), its domain is not (-∞,∞).

You will need to find the domain of the function, namely the interval of which the expression under the square-root sign stays positive. The said expression is a cubic and crosses the x-axis only once, so it is easy to find the zero using Newton-Raphson method. In case you have difficulties, it is around -43.

- Calculus -
**MathMate**, Sunday, November 22, 2009 at 9:56amAdditional note:

do not forget to test the first two critical points (where f'(x)=0) for maximum or minimum.

- Calculus -
**Salman**, Sunday, November 22, 2009 at 10:05amwhat is the exact value of the -43 term? i cant find it

- Calculus -
**MathMate**, Sunday, November 22, 2009 at 10:24amTell me what values you've got so far.

It should be quite straight forward, because the slope is almost uniform in that stretch.

Perhaps you didn't get the right derivative, or formula.

- Calculus -
**MathMate**, Sunday, November 22, 2009 at 10:29amOh, it's not a factoring process, the third point is to be solved using Newton-Raphson. The first two are the solutions of the quadratic.

- Calculus -
**Salman**, Sunday, November 22, 2009 at 11:26amI cant find the value of x1. im getting it around -43.2423, but this answer is not correct

- Calculus -
**MathMate**, Sunday, November 22, 2009 at 6:39pmMine agrees with yours up to -43.24...

To how many figures are you supposed to calculte, and how many lives do you have left (assuming you have a computer exercise).