Answer:
Graph = Cardioid
Axis of symmetry = y-axis
Critical points= [tex]\frac{\pi}{2} , \frac{3\pi }{2}[/tex]
Step-by-step explanation:
General equation for this type of cardioid is:
a ± b sinθ
Condition for a cardioid = [tex]\frac{a}{b} = 1[/tex]
Axis of symmerty according to the graph of 2 + 2 sinθ is along y-axis.
Critical points:
r = 2 + 2 sinθ ⇒ r = 2(1 + sinθ) ⇒ r' = 2 cosθ
∵derivative of 1 + sinθ = cosθ
For finding critical point the derivative is equal to zero,
2 cosθ = 0 ⇒ cosθ = 0
the value of cosθ is equal to zero at intervals: [tex]\frac{\pi}{2} , \frac{3\pi }{2}[/tex]
So, critical points = [tex]\frac{\pi}{2} , \frac{3\pi }{2}[/tex]
