4. (10 points) Find all relative and absolute extrema of the function \[ f(t)=\frac{1}{2} t^{4}+\frac{10}{3} t^{3} \] with domain \( (-\infty,+\infty) \). Then the same function with domain \( [-2,+\infty) \)

1. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the functions: (a) \( F(r)=\int_{0}^{r} \sqrt{x^{2}+4} d x \)

9. \( \int \frac{(x \sqrt{x}-3)^{2}}{x^{3}} d x \)

11. \( \int x^{2}(1+2 x) d x \)

A certain tranquilizer decays exponentially in the bloodstream and has a half-life of 22 hours. How long with it take for the drug to decuy to \( 82 \% \) of the original dose? a) step 1 : Find \( K \) (Round to four decimalpleas) b) step 2 : Use \( k \) to determine how longlinhours) it will take for the drug to decay to \( 82 \% \) of the original dose. (Round to one decinalplace)

Question For the equation given below, one could use Newton's method as a way to approximate the solution. Find Newton's formula as \( x_{n+1}=F\left(x_{n}\right) \) that would enable you to do so. \[ \ln (x)-9=-7 x \] Sorry, that's incorrect. Try again? \( x_{n+1}=\square \)