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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Solve.31 = 4x - 5
A. {12} B. {9} C. {36} D. {32}
Provide an appropriate response.Consider the linear equation in three variables x - y + z = 6. Find a pair of linear equations that, when considered together with the given equation, will form a system having no solution.
What will be an ideal response?
Use a Venn Diagram and the given information to determine the number of elements in the indicated set.n(U) = 147, n(A) = 48, n(B) = 68, n(A ? B) = 19, n(A ? C) = 22, 
and 
Find n(C).
A. 26 B. 14 C. 30 D. 46
Find the opposite of the integer.0
A. 1 B. 0 C. -1 D. does not exist