(Solved): 3. Consider the function B(t)=2tlnt+4fort0. Assume that the function B(t) represents the b ...

3. Consider the function $$B(t)=2t\ln t+4\text{ for }t?0\text{. }$$ Assume that the function $$B(t)$$ represents the biomass of an insect population ( ica mass of the population) in kilograms at time $$t$$ in months. continues on the next page 1 (a) Determine the times when the biomass increakes and the timer when the biomas decreases. (b) Determine the time when the biomas is maximal and the maximal biomass. Fotmulate your final answer in a complete sentence and include the units. 4. Suppose that $$f(x)$$ is a function with the following derivatives $$f^{?}(x)=e^2\left(x^2?4x?1\right)\text{. }{f}^{??}(x)=e^{?}\left(x^2?2x?8\right)$$ (a) Determine the critical points of $$f$$ (you may need the formula $$\frac{?46\sqrt{2?}\text{ met }}{29}$$ or the caleulator at some point) and then determine the intervals on which $$f$$ increases/decreases. (b) Determine the intervals on which $$f$$ is concave up/down. (c) Determine the $$x$$-values of the relative minimums, relative maximums, and the inllection points.