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Home / Calculus I / Applications of Derivatives / Finding Absolute Extrema
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Section 4.4 : Finding Absolute Extrema

For each of the following problems determine the absolute extrema of the given function on the specified interval.

  1. f(z)=2z416z3+20z27 on [2,6]
  2. f(z)=2z416z3+20z27 on [2,4]
  3. f(z)=2z416z3+20z27 on [0,2]
  4. Q(w)=20+280w3+75w412w5 on [3,2]
  5. Q(w)=20+280w3+75w412w5 on [1,8]
  6. g(z)=812z525z6+907z7 on [1,1]
  7. g(t)=3t420t3132t2+672t4 on [5,8]
    Note : Depending upon your factoring skills this may require some computational aids.
  8. g(t)=3t420t3132t2+672t4 on [2,8]
    Note : Depending upon your factoring skills this may require some computational aids.
  9. V(x)=14x3+11x24x+3 on [1,1]
  10. a(t)=42t26t33t4 on [2,1]
  11. h(x)=8+3x+7x2x3 on [1,5]
  12. f(x)=3x420x3+6x2+120x+5 on [1,5]
    Note : This problem will require some computational aids.
  13. h(v)=v5+v4+10v315 on [3,2]
  14. g(z)=(z3)5(2z+1)4 on [1,3]
  15. R(q)=(q+2)4(q28)2 on [4,1]
  16. h(t)=34tt2+1 on [2,4]
  17. g(x)=6+9x+x21+x+x2 on [6,0]
  18. f(t)=(t325t)23 on [2,6]
  19. F(t)=2+t25(1+t+t2) on [2,1]
  20. Q(w)=(6w2)3w24 on [5,12]
  21. g(x)=3cos(2x)5x on [0,6]
  22. s(w)=3w10sin(w3) on [10,38]
  23. f(x)=7cos(x)+2x on [5,4]
  24. h(x)=xcos(x)sin(x) on [15,5]
  25. g(z)=z2e1z on [12,52]
  26. P(t)=(6t+1)e8tt2 on [1,3]
  27. f(x)=e5+9x+e13x+6 on [1,0]
  28. h(y)=e6y38y2 on [12,1]
  29. Z(t)=ln(t2+t+3) on [2,2]
  30. f(x)=x4ln(x2+x+2) on [1,9]
  31. h(t)=ln(t2t+1)+ln(4t) on [1,3]