Justify that you have found the requested point by analyzing an appropriate derivative. x=ln⁡(5t) y=ln⁡(4t2) 0&lt;t≤10 Rightmost point.

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Justify that you have found the requested point by analyzing an appropriate derivative.  x=ln⁡(5t)  y=ln⁡(4t2)  0&amp;lt;t≤10  Rightmost point.

Thomas Lynn · Accepted Answer

Step 1  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 results, we have that  dxdt=15t×5=1t⇒dxdt≠0  for 0&amp;lt;t≤10  Since we know that 1t&amp;gt;0 for 0&amp;lt;t≤10, then we have that dxdt&amp;gt;0 for 0&amp;lt;t≤10.  According to the previous results, we can conclude that the function x=ln⁡(5t) is increasing for 0&amp;lt;t≤10, which means that the function x=ln⁡(5t), where 0&amp;lt;tleq10ZSK, has the maximum at point t=10  Since in this exercise we have that y=ln⁡(4t2), where 0&amp;lt;t≤10, then we have that  x(10)=ln⁡(5×10)=ln⁡(50)≈3.912  y(10)=ln⁡(4×102)=ln⁡(400)≈5.991  Which means that the rightmost point of the curve is equal to  (ln⁡(50), ln⁡(400))≈(3.912, 5.991)

Justify that you have found the requested point by analyzing

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