Does f Have a Local Extrema at x = 0?Date: 07/10/2003 at 16:29:40 From: Sara Subject: I'm horrible with trig f(x) = (x^3)/6 + (x^2)/2 + cosx - 1 Does f have a local extremum at x = 0? Date: 07/10/2003 at 17:54:01 From: Doctor Jaffee Subject: Re: I'm horrible with trig Hi Sara, If a function is differentiable for all values of x (which your function is), all that you have to worry about is if the first derivative is equal to zero and the second derivative isn't. The reason is that if the first derivative equals zero, then the tangent line is horizontal, so the point is either a maximum, a minimum, or possibly an inflection point. If the second derivative is zero, then the point is an inflection point. So, calculate f'(0) and f"(0) and you should have the answer to your question. Give it a try and if you want to check your solution with me or if you have difficulties or other questions write back to me and I'll try to help you some more. Good luck, - Doctor Jaffee, The Math Forum http://mathforum.org/dr.math/ |
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