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

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

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. \

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

Find $d y / d x$ at the indicated point for the equation. \

$$x=y^3-7 y^2+2,(-4,1) \quad$$

Use the Quotient Rule to differentiate the function. \

$$g(x)=\dfrac{\sin x}{x^2}$$

Find $d y / d x$ by implicit differentiation. \

$$x^3-2 x^2 y+3 x y^2=38$$

Find the derivative by the limit process. \

$$f(x)=3$$

Find the derivative of the function. \

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

Find the derivative of the function. \

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

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.

Use a graphing utility to graph the function and its tangent line at the point.

Find an equation of the tangent line to the graph of $f$ at the indicated point

Use the utility to graph the function and its tangent line in the same viewing window.
$s(t)=\dfrac{(4-2 t) \sqrt{1+t}}{3}, \quad\left(0, \dfrac{4}{3}\right)$

Find an equation of the tangent line to the graph of the function at the given point
$s(t)=\dfrac{(4-2 t) \sqrt{1+t}}{3}, \quad\left(0, \dfrac{4}{3}\right)$

Use a graphing utility to find the derivative of the function at the given point
$s(t)=\dfrac{(4-2 t) \sqrt{1+t}}{3}, \quad\left(0, \dfrac{4}{3}\right)$