4.4-bo'lim : Mutlaq ekstremallarni topish

Quyidagi masalalarning har biri uchun berilgan funksiyaning belgilangan oraliqdagi mutlaq ekstremalini aniqlang.

1. \(\left[ { - 2,6} \right]\) da \(f\left( z \right) = 2{z^4} - 16{z^3} + 20{z^2} - 7\)
2. \(\left[ { - 2,4} \right]\) da \(f\left( z \right) = 2{z^4} - 16{z^3} + 20{z^2} - 7\)
3. \(\left[ {0,2} \right]\) da \(f\left( z \right) = 2{z^4} - 16{z^3} + 20{z^2} - 7\)
4. \(\left[ { - 3,2} \right]\) da \(Q\left( w \right) = 20 + 280{w^3} + 75{w^4} - 12{w^5}\)
5. \(\left[ { - 1,8} \right]\) da \(Q\left( w \right) = 20 + 280{w^3} + 75{w^4} - 12{w^5}\)
6. \(\displaystyle g\left( z \right) = 8 - 12{z^5} - 25{z^6} + \frac{90}{7}{z^7}\), \(\left[ { - 1,1} \right]\)
7. \(g\left( t \right) = 3{t^4} - 20{t^3} - 132{t^2} + 672t - 4\), \(\left[ { - 5,8} \right]\)
   Eslatma: Faktoring qobiliyatingizga qarab, bu ba'zi hisoblash vositalarini talab qilishi mumkin.
8. \(g\left( t \right) = 3{t^4} - 20{t^3} - 132{t^2} + 672t - 4\), \(\left[ { - 2,8} \right]\)
   Eslatma: Faktoring qobiliyatingizga qarab, bu ba'zi hisoblash vositalarini talab qilishi mumkin.
9. \(V\left( x \right) = 14{x^3} + 11{x^2} - 4x + 3\), \(\left[ { - 1,1} \right]\)
10. \(a\left( t \right) = 4 - 2{t^2} - 6{t^3} - 3{t^4}\), \(\left[ { - 2,1} \right]\)
11. \(h\left( x \right) = 8 + 3x + 7{x^2} - {x^3}\), \(\left[ { - 1,5} \right]\)
12. \(f\left( x \right) = 3{x^4} - 20{x^3} + 6{x^2} + 120x + 5\), \(\left[ { - 1,5} \right]\)
    Eslatma: Bu muammoni hal qilish uchun ba'zi hisoblash vositalari kerak bo'ladi.
13. \(h\left( v \right) = {v^5} + {v^4} + 10{v^3} - 15\), \(\left[ { - 3,2} \right]\)
14. \(g\left( z \right) = {\left( {z - 3} \right)^5}{\left( {2z + 1} \right)^4}\), \(\left[ { - 1,3} \right]\)
15. \(R\left( q \right) = {\left( {q + 2} \right)^4}{\left( {{q^2} - 8} \right)^2}\), \(\left[ { - 4,1} \right]\)
16. \(\displaystyle h\left( t \right) = \frac{{3 - 4t}}{{{t^2} + 1}}\), \(\left[ { - 2,4} \right]\)
17. \(\displaystyle g\left( x \right) = \frac{{6 + 9x + {x^2}}}{{1 + x + {x^2}}}\)-da \(\left[ { - 6,0} \right]\)
18. \(\left[ {2,6} \right]\) da \(f\left( t \right) = {\left( {{t^3} - 25t} \right)^{\frac{2}{3}}}\)
19. \(F\left( t \right) = 2 + {t^{\frac{2}{5}}}\,\left( {1 + t + {t^2}} \right)\), \(\left[ { - 2,1} \right]\)
20. \(Q\left( w \right) = \left( {6 - {w^2}} \right)\,\,\,\sqrt[3]{{{w^2} - 4}}\), \(\displaystyle \left[ { - 5,{\frac{1}{2}}} \right]\)
21. \(g\left( x \right) = 3\cos \left( {2x} \right) - 5x\), \(\left[ {0,6} \right]\)
22. \(\displaystyle s\left( w \right) = 3w - 10\sin \left( {{\frac{w}{3}}} \right)\), \(\left[ {10,38} \right]\)
23. \(\left[ { - 5,4} \right]\) da \(f\left( x \right) = 7\cos \left( x \right) + 2x\)
24. \(\left[ { - 15, - 5} \right]\) da \(h\left( x \right) = x\cos \left( x \right) - \sin \left( x \right)\)
25. \(g\left( z \right) = {z^2}{{\bf{e}}^{1 - z}}\), \(\left[ {\displaystyle - {\frac{1}{2}},{\displaystyle \frac{5}{2}}} \right]\)
26. \(\left[ { - 1,3} \right]\)-da \(P\left( t \right) = \left( {6t + 1} \right){{\bf{e}}^{8t - {t^{\,2}}}}\)
27. \(f\left( x \right) = {{\bf{e}}^{5 + 9x}} + {{\bf{e}}^{1 - 3x}} + 6\), \(\left[ { - 1,0} \right]\)
28. \(\left[ { - {\displaystyle \frac{1}{2}},1} \right]\) da \(h\left( y \right) = {{\bf{e}}^{6{y^{\,3}} - 8{y^{\,2}}}}\)
29. \(Z\left( t \right) = \ln \left( {{t^2} + t + 3} \right)\), \(\left[ { - 2,2} \right]\)
30. \(f\left( x \right) = x - 4\ln \left( {{x^2} + x + 2} \right)\), \(\left[ { - 1,9} \right]\)
31. \(h\left( t \right) = \ln \left( {{t^2} - t + 1} \right) + \ln \left( {4 - t} \right)\), \(\left[ {1,3} \right]\)