BC Derivatives Test #1

Differentiate:

 $y=\frac{1+\cos x}{1-\cos x}$  

• -1

• -2cscx

• 2cscx

•  $\frac{-2\sin x}{\left(1-\cos x\right)^2}$  

Find an equation of the tangent line to the graph of

 $f\left(x\right)=\frac{1}{x-1}$   at the point (2,1)

• x + y  = 3

• x - y = 1

•  $y-1=-\frac{\left(x-2\right)}{\left(x-1\right)^2}$  

• x + y = 6

Use the graph to determine all x-values at which the function is not differentiable.

• a, b, c, d, e, f, and g

• b and d

• a and f

• a, f, and g

• None of these

Differentiate:

 $y=\frac{3x}{x^2+1}$  

•  $\frac{3\left(1-x^2\right)}{\left(1+x^2\right)^2}$  

•  $\frac{3}{1+x^2}$  

•  $\frac{3}{2x}$  

•  $\frac{3x^2-3}{\left(1+x^2\right)^2}$  

• None of these

 $If\ y=\frac{2x+3}{3x+2},\ then\ \frac{\text{d}x}{\text{d}y}=$  

•  $\frac{2}{3}$  

•  $\frac{12x+13}{\left(3x+2\right)^2}$  

•  $\frac{12x-13}{\left(3x+2\right)^2}$  

•  $\frac{5}{\left(3x+2\right)^2}$  

•  $\frac{-5}{\left(3x+2\right)^2}$  

Find the equation of the tangent line to the graph of f(x) = xsinx when x = 0.

• y = 0

• f '(x) = 0

• y = xcosx + sinx

• y = x

The graph of y = f(x) is given. On which intervals is

 $\frac{\text{d}x}{\text{d}y}>0$  
I.    a < x < b
II.   b < x < c
III.  c < x < d

• I only

• II only

• III only

• I and III

• II and III

 $If\ F\left(x\right)=x\sin x,\ then\ find\ F\ '\left(\frac{3\pi}{2}\right).$  

• 0

• 1

• -1

•  $\frac{3\pi}{2}$  

•  $-\frac{3\pi}{2}$  

Given that s(t) = -10t² + 4, where s is measured in feet and t is measured in seconds. What is s'(t) when t = 2?

• -10 ft/sec

• -40 ft/sec

• -36 ft/sec

• 44 ft/sec

If f(2) = -3, f '(2) = 3/4, write the equation of the normal line.

• $y-3=\frac{3}{4}\left(x-2\right)$

• $y+3=\frac{3}{4}\left(x-2\right)$

• $y+3=\frac{4}{3}\left(x-2\right)$

• $y+3=-\frac{4}{3}\left(x-2\right)$

• $y-3=-\frac{4}{3}\left(x-2\right)$