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 ? ?.
You might also like to view...
Find the Cartesian coordinates of the given point.
A. (14
, 14
)
B. (14, 14)
C. (7
, 7
)
D. (7
, 7)
Provide an appropriate response.A bottle contains 1.5 L of drinking water. How many deciliters is this?
A. 0.15 dL B. 150 dL C. 0.015 dL D. 15 dL
Provide an appropriate response.Solve the following system of equations using the substitution method: 2j - k = 3?k = 2 + j
Fill in the blank(s) with the appropriate word(s).
Determine whether the equation is a function.y = x4
A. function B. not a function