Provide an appropriate response.Consider the quartic function f(x) = ax4 + bx3 + cx2 + dx + e, a ? 0. Must this function have at least one critical point? Give reasons for your answer. (Hint: Must 
for some x?) How many local extreme values can f have?
What will be an ideal response?
Yes. The derivative is cubic: 4ax3 + 3bx2 + 2cx + d. The derivative approaches -? as x approaches 
and it approaches ? as x approaches ?. By the Intermediate Value Theorem, f'(x) must equal zero at at least one point on the interval -? ? x ? ?.
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Give an appropriate answer.Using the following graph, find an Euler path that starts with vertex B.
A. B ? E? D ? A ? C ? E ? D B. B ? A ? D ? E ? C C. B ? A? D ? E ? B ? C ? A ? E ? C ? D D. No Euler path exists.
Provide an appropriate response.You have a choice of two banks. One bank pays interest at 5.54% compounded monthly and the other bank pays interest at 5.53% compounded daily (365 times a year). Which is the better choice? How much more would you make in one year if you deposited $1000?
Fill in the blank(s) with the appropriate word(s).
Solve.In an office building, 18 offices are currently being unrented. This represents 8% of the total units. How many offices are there in the building?
A. 144 offices B. 22.5 offices C. 2250 offices D. 225 offices
Write out the first five terms of the sequence.{sn} = {n2 - n}
A. s1= 2, s2= 6, s3= 12, s4= 20, s5= 30 B. s1= 0, s2= 3, s3= 8, s4= 15, s5= 24 C. s1= 0, s2= 2, s3= 6, s4= 12, s5= 20 D. s1= 1, s2= 4, s3= 9, s4= 16, s5= 25