Question

asked 2021-05-14

Use the given graph off over the interval (0, 6) to find the following.

a) The open intervals on whichfis increasing. (Enter your answer using interval notation.)

b) The open intervals on whichfis decreasing. (Enter your answer using interval notation.)

c) The open intervals on whichfis concave upward. (Enter your answer using interval notation.)

d) The open intervals on whichfis concave downward. (Enter your answer using interval notation.)

e) The coordinates of the point of inflection. \((x,\ y)=\)

a) The open intervals on whichfis increasing. (Enter your answer using interval notation.)

b) The open intervals on whichfis decreasing. (Enter your answer using interval notation.)

c) The open intervals on whichfis concave upward. (Enter your answer using interval notation.)

d) The open intervals on whichfis concave downward. (Enter your answer using interval notation.)

e) The coordinates of the point of inflection. \((x,\ y)=\)

asked 2021-05-08

Find the points on the cone \(z^2 =x^2+y^2\) that are closest tothe point (2, 2,0).

asked 2021-06-09

Use the table of values of \(f(x, y)\) to estimate the values of \(fx(3, 2)\), \(fx(3, 2.2)\), and \(fxy(3, 2)\).

\(\begin{array}{|c|c|}\hline y & 1.8 & 2.0 & 2.2 \\ \hline x & & & \\ \hline 2.5 & 12.5 & 10.2 & 9.3 \\ \hline 3.0 & 18.1 & 17.5 & 15.9 \\ \hline 3.5 & 20.0 & 22.4 & 26.1 \\ \hline \end{array}\)

\(\begin{array}{|c|c|}\hline y & 1.8 & 2.0 & 2.2 \\ \hline x & & & \\ \hline 2.5 & 12.5 & 10.2 & 9.3 \\ \hline 3.0 & 18.1 & 17.5 & 15.9 \\ \hline 3.5 & 20.0 & 22.4 & 26.1 \\ \hline \end{array}\)

asked 2021-05-03

Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y:

\(f(x,y)=\begin{cases}xe^{-x(1+y)} & x\geq0\ and\ \geq0\\ 0 & otherwise \end{cases}\)

a) What is the probability that the lifetime X of the first component exceeds 3?

b) What are the marginal pdf's of X and Y? Are the two lifetimes independent? Explain.

c) What is the probability that the lifetime of at least one component exceeds 3?

\(f(x,y)=\begin{cases}xe^{-x(1+y)} & x\geq0\ and\ \geq0\\ 0 & otherwise \end{cases}\)

a) What is the probability that the lifetime X of the first component exceeds 3?

b) What are the marginal pdf's of X and Y? Are the two lifetimes independent? Explain.

c) What is the probability that the lifetime of at least one component exceeds 3?