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Solve the given problems by finding the appropriate derivative.The energy $E$ (in $\mathrm{J}$ ) dissipated by a certain resistor after $t$ seconds is given by $E=\ln (t+1)-0.25 t .$ At what time is the energy dissipated the greatest?

$$3.0 \mathrm{s}$$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 8

Applications

Derivatives

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we need to find the time at which the energy E. He dissipated by senate resistor is the greatest. So we're given the punch and eve he is equal to is equal to Ellen. She plus one -0.25 T. So to find the greatest valuable function first we need to find the first derivative and quote that you know. And we can find that the first deliberate is using the formally DDT. Uh huh. Oh what so D. D. T. Over Ellen of you is equal to one over years time to be on the Bt. Um for here we could say U. is equal to T. Plus one. And we get the E. O. D. Ti that will be equal to 1, 1/1 1/2 plus one- Air .5- Their .25. So then we can set this to be equal to zero and then to self a team And he will be equal to three. So now to find the second derivative to find the second president, once he is equal to three, The second derivative will be one Over T. Plus one. Great. That is equal to negative one over four square Which is negative 1/16. Now, since the value of our second derivative for T. Is equal to three, we can find the maximum value. Uh huh. Once he is equal to three so um is equal to Ln of T plus one -0.5 -0.2. And this happens when C. is equal to three

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