Inflection Points and Local Minimums

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SUMMARY

The discussion focuses on solving polynomial equations to determine coefficients that yield specific inflection points and local extrema. For Problem One, the polynomial is defined as f(x) = ax4 + bx3 - cx2 - dx - e, with inflection points at ((√3)/3, -7.5752) and (-(√3)/3, -0.647009), and a local minimum at (1.26255, -11.8696). In Problem Two, the polynomial f(x) = qx4 - rx3 - sx2 + tx + u requires coefficients q, r, s, t, and u to achieve local minimums at (-0.398238, -0.457621) and (1.20556, -3.46602), and a local maximum at (0.130182, 0.069458). A suggested solution for Problem Two includes q = 4, r = 5, s = 3, t = 1, and u = 0.

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Students and professionals in mathematics, particularly those studying calculus, polynomial functions, and optimization techniques. This discussion is also beneficial for anyone involved in computational mathematics or algorithm development.

carbonsteel
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1. Use the following equations to fill in the missing numbers. The correct addition and subtraction signs have already been entered.

PROBLEM ONE:
f(x) = ax4 + bx3 - cx2 - dx - e

Find values of a,b,c,d, and e so that the function has inflection points at ((v3)/3, -7.5752) and (-(v3)/3, -.647009) and has a local minimum at (1.26255, -11.8696).


PROBLEM TWO:
f(x) = qx4 - rx3 - sx2 +tx + u

Find values of q, r, s, t, and u so that the function has local minimums at (-.398238, -.457621) and (1.20556, -3.46602) also so the function has a local maximum at (.130182, .069458).




2. See above



3. ?

I never took calculus. Need assistance in solving these problems to solve a puzzle. I need to know what the values are for a, b, c, d, e and q, r, s, t, u.

Thank you.
 
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carbonsteel said:
PROBLEM TWO:
f(x) = qx4 - rx3 - sx2 +tx + u

Find values of q, r, s, t, and u so that the function has local minimums at (-.398238, -.457621) and (1.20556, -3.46602) also so the function has a local maximum at (.130182, .069458).

Thank you.

Were you really given those decimals or have you rounded something off?

Try q = 4, r = 5, s = 3, t = 1, u = 0
 

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