Justify that you have found the requested point by analyzing an appropriate derivative. x=2sin⁡t, y=cos⁡t, 0≤t≤π Rightmost point.

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Justify that you have found the requested point by analyzing an appropriate derivative. x=2sin⁡t,  y=cos⁡t,  0≤t≤π  Rightmost point.

nick1337 · Accepted Answer

Step 1 Since we need to find the lowest point of the curve, we need to find the minimum of the function x=2sin⁡t where 0≤t≤π We know that function x has a relative maximum at point t=t0 if we have that dxdt(t0)=0 dxdt&amp;gt;0 for t&amp;lt;t0, and dxdt&amp;lt;0 for t&amp;gt;t0. We also know that if function x has one relative maximum at point t=t0, then function x has the maximum at point t=t0 Using the previous reults, we have that dxdt=2cos⁡t⇒dxdt(π2)=0 Because we know that cos⁡(π2)=0. Since we know that cos⁡t&amp;gt;0 for 0≤t≤π2 and cos⁡t&amp;lt;0 for π2&amp;lt;t&amp;lt;π, then using the previous results, we can conclude that dxdt&amp;gt;0 for 0≤t&amp;lt;π2 and dxdt&amp;lt;0 for π2&amp;lt;t≤π. According to the previous results, we can conclude that the function x=2sin⁡t, where 0≤t≤π, has the maximum at point t=π2. ince in this exercise we have that y=cos⁡t, where 0≤t≤π, then we have that x(π2)=2sin⁡(π2)=2×1=2 y(π2)=cos⁡(π2)=0 Which means that the rightmost point of the curve is equal to (2, 0)

Justify that you have found the requested point by analyzing

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