Compare and contrast genetic drift and natural selection as mechanisms of evolution.

Compute the directional derivative of f at the given point in the direction of the indicated vector. $f(x, y)=x^{2}+x y^{2},(2,1), \mathbf{u}$ in the direction of $\langle 3,-2\rangle$

What is the difference between the meanings of the terms evolution and natural selection? _________________________________

Find the directional derivative of the given function at the given point in the indicated direction. $F(x, y, z)=\sqrt{x^{2} y+2 y^{2} z} ;(-2,2,1)$, in the direction of the negative z-axis.

Given that

$$f_x(-5,1)=-3$$

and

$$f_y(-5,1)=2$$

, find the directional derivative of f at P(−5, 1) in the direction of the vector from P to Q(−4, 3).

What is one factor that affects natural selection? Give an example.

Find the directional derivative at the point $P$ in the direction indicated. $f(x, y, z)=A x^2+B x y z+C y^2$ at $P(1,2,1)$ in the direction of $A \mathbf{i}+B \mathbf{j}+C \mathbf{k}$

Find the directional derivative at the point $P$ in the direction indicated. $f(x, y)=\ln \left(x^2+y^2\right)$ at $P(0,1)$ in the direction of $8 \mathbf{i}+\mathbf{j}$.

How does the development of antibiotic resistance in a population of bacteria support the theory of evolution through natural selection?

Let $f(x, y)=\tan ^{-1} \frac{y}{x}$. Find the directional derivative of f at (1, 2) in the direction that makes an angle of $\frac{\pi}{3}$ with the positive x-axis.

$______________________$ occurs when natural selection favors the survival of close relatives.

Find the directional derivative of the function at $P$ in the direction of $v$.

$$w=y^2+x z, \quad(1,2,2), \quad \mathbf{v}=2 \mathbf{i}-\mathbf{j}+2 \mathbf{k}$$

Show that the function f(x, y) = ∛xy is continuous and the partial derivatives fx and fy exist at the origin but the directional derivatives in all other directions do not exist.

Find the directional derivative of f at P in the direction of a vector making the counterclockwise angle θ with the positive x-axis. f(x, y)=sinh x coshy; P(0, 0);

$$\theta = \pi$$