**PROBLEM 2.**Suppose that

*x*and

*y*are both functions of time,

*t*, that $x = x(t)$, and $y = y(t)$, and the function $z = z(t)$ of time is given by $z = f(x, y)$, so that Use the chain rule to express in terms of

**PROBLEM 3.**Suppose that a beetle is crawling along the graph of the curve

$z = f(x, y) = 8$

so that the rate of increase of x for the beetle is 6 units per second at the instant the beetle passes through the point (4, 2). What is the rate of increase of $z$ for the beetle at the instant the beetle passes through the point (4, 2)?**PROBLEM 4.**Suppose that a beetle is crawling along the graph of the curve

$z = f(x, y) = 8$

so that the rate of increase of x for the beetle is 6 units per second at the instant the beetle passes through the point (4, 2). What is the rate of increase of $y$ for the beetle at the instant the beetle passes through the point (4, 2)?**PROBLEM 5.**What is at the point (4, 2) on the curve $z = f(x, y) = 8$?

**PROBLEM 7.**What are the critical points of $g$ on the interval

**PROBLEM 8.**What is on the interval $−1 < x < 12$?

**PROBLEM 9.**What are the inflection points of &g& on the interval &−1 < x < 12&?

**PROBLEM 10.**What is the value of $x$ for which $g(x)$ is maximum for $−1 ≤ x ≤ 12$?

**Calclate the following integrals and derivatives.**

**ANSWERS:**

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