Provide an appropriate response.Does the curve y = (x + 3)3 have any horizontal tangents? If so, where? Give reasons for your answer.
What will be an ideal response?
The curve y = (x + 3)3 has a horizontal tangent at x = -3. The derivative of the curve is 
which equals zero at x = -3. A curve has a horizontal tangent wherever its derivative equals zero.
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Factor the trinomial.10y2 - 23y + 12
A. (10y + 3)(y + 4) B. (2y + 3)(5y + 4) C. (2y - 3)(5y - 4) D. Cannot be factored
Transform the equation to a form without an xy-term by a rotation of axes and then identify the curve.x2 + 2xy + y2 - 4x + 4y = 0
A. x'2 + 2
y' = 0; parabola
B. x'2 + 2
y' = 0; ellipse
C. x'2 - 2
y'2 = 0; hyperbola
D. x'2 - 2
y' = 0; parabola
Provide an appropriate response.Graph the equation -4x + 2y = 8 using the intercepts procedure.
A. 
B. 
C. 
D. 
Write the interval as an inequality involving x, and illustrate the inequality using the real number line.(-?, -2)
A. x ? -2
B. x < -2
C. x ? -2
D. x < -2