# Math Help - maxima and minima

1. ## maxima and minima

Hi friends,

I am trying to find the maxima and minima of

f(x) = 12x^6 – 4x^4 + 15x^3 –1.

but after calculating f'(x) I am unable to solve it. Please guide me...

2. Originally Posted by mailquark
Hi friends,

I am trying to find the maxima and minima of

f(x) = 12x^6 – 4x^4 + 15x^3 –1.

but after calculating f'(x) I am unable to solve it. Please guide me...
The solutions are either x = 0 or solutions to $72x^3 - 16x + 45=0$.

The cubic does not have easily found solutions (although it can be solved). What makes you think exact solutions are required?

3. The question is in my book. I tried a lot almost 30 mins to solve this cubic... but could not....

4. Originally Posted by mailquark
The question is in my book. I tried a lot almost 30 mins to solve this cubic... but could not....
State the question exactly as it's worded in your book.

5. For the following function, find a point of maxima and a point of minima, if these exist
f(x) = 12x^6 – 4x^4 + 15x^3 –1

6. Originally Posted by mailquark
For the following function, find a point of maxima and a point of minima, if these exist
f(x) = 12x^6 – 4x^4 + 15x^3 –1
There's a stationary point of inflection at (0, -1).

There's a minimum turning at $x \approx -0.941$. If you want to use the cubic formula to solve for x (at least it's a depressed cubic so that's a start) be my guest. There's no simple way of getting the exact value of x.

Does the book have an answer at the back?

7. No its collection of previous year question papers... I am practicing as exams are coming in December... If you can guide on this question I will be thankful.

8. Originally Posted by mailquark
No its collection of previous year question papers... I am practicing as exams are coming in December... If you can guide on this question I will be thankful.

If you want an exact value for the x-coordinate of the minimum turning point, solve the cubic equation by following the process given here: Cubic Formula -- from Wolfram MathWorld

Good luck substituting this exact value into y = f(x) to get the y-coordinate.

9. Thanks a lot for giving for time...

actually I am studying part time through distant learning and there is no instructor to guide so i thought anyone here can help. hence i posted two questions which only i was not able to solve in last 4 question papers. one is this question and another is

http://www.mathhelpforum.com/math-he...-equation.html

regards
Kr.

PS: I also tried formula given here http://en.wikipedia.org/wiki/Cubic_equation