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

Answered

2022-01-17

Justify that you have found the requested point by analyzing an appropriate derivative. x=2sint,
y=cost,
0tπ
Rightmost point.

Answer & Explanation

nick1337

nick1337

Expert

2022-01-19Added 573 answers

Step 1 Since we need to find the lowest point of the curve, we need to find the minimum of the function x=2sint where 0tπ We know that function x has a relative maximum at point t=t0 if we have that dxdt(t0)=0 dxdt>0 for t<t0, and dxdt<0 for t>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=2costdxdt(π2)=0 Because we know that cos(π2)=0. Since we know that cost>0 for 0tπ2 and cost<0 for π2<t<π, then using the previous results, we can conclude that dxdt>0 for 0t<π2 and dxdt<0 for π2<tπ. According to the previous results, we can conclude that the function x=2sint, where 0tπ, has the maximum at point t=π2. ince in this exercise we have that y=cost, where 0tπ, 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)

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