Refrigeration The temperature $T$ of food put in a freezer is

$$T=\frac{700}{t^2+4 t+10}$$

where $t$ is the time in hours. Find the rate of change of $T$ with respect to $t$ at each of the following times.
(a) $t=1$ (b) $t=3$ (c ) $t=5$ (d) $t=10$

Use a computer algebra system to find the second derivative of the function. \

$$g(x)=x^3 \ln x$$

Horizontal Tangent Line Determine the point(s) in the interval $(0,2 \pi)$ at which the graph of $f(x)=2 \cos x+\sin 2 x$ has a horizontal tangent line.

Use a computer algebra system to find the second derivative of the function. \

$$h(x)=x \sqrt{x^2-1}$$

Use a computer algebra system to find the second derivative of the function. \

$$g(\theta)=\tan 3 \theta-\sin (\theta-1)$$

Use the utility to graph the function and its tangent line in the same viewing window. \

$$y=\left(t^2-9\right) \sqrt{t+2}, \quad(2,-10)$$

Find an equation of the tangent line to the graph of the function at the given point \

$$y=\left(t^2-9\right) \sqrt{t+2}, \quad(2,-10)$$

Use a graphing utility to find the derivative of the function at the given point \

$$y=\left(t^2-9\right) \sqrt{t+2}, \quad(2,-10)$$

Use a computer algebra system to find the second derivative of the function.
$g(x)=\dfrac{6 x-5}{x^2+1}$

Find the derivative by the limit process. \

$$f(x)=3$$

Consider the linear function $y=a x+b$. If $x$ changes at a constant rate, does $y$ change at a constant rate? If so, does it change at the same rate as $x$ ? Explain.

Find the derivative of the function. \

$$f(x)=\left(9-x^2\right)^{2 / 3}$$

Find the derivative of the function. \

$$f(x)=6 x-5 e^x$$

Approximate the zero(s) of the function. Use Newton's Method and continue the process until two successive approximations differ by less than $0.001$. Then find the zero(s) using a graphing utility and compare the results. \

$$f(x)=x+\sin (x+1)$$