Derivative Apps and Trig Warmup

The position of a moving particle at time t is given by the function

 $s\left(t\right)=t^3-8t^2+5t+1$   

Determine the times at which the point is stationary.

•  $t=\frac{1}{3},\ 5$  

•  $t=\frac{1}{3}$  

•  $t=\frac{1}{3},\ -5$  

•  $t=-5$  

If an object is dropped from a tower 400 feet above the ground, its distance above the ground after t seconds is given by g(t)=400-16t² feet. Find the velocity of the object on impact.

• 165sec/ft

• 160ft/sec

• 400ft/sec

• 165ft/sec

Find the equation of the line that is tangent to the curve

 $y=-\frac{1}{3}\cos\left(3x\right)$  when  $x=\frac{\pi}{6}$  .

•  $y=x-\frac{\pi}{6}$  

•  $\prod_x^y\oint_x^y\int_x^y\sum_x^y\lfloor x\rfloor\lceil x\rceil\updownarrow$  

•  $y=-x+\frac{\pi}{6}$  

• y=x

 $y=\sin x-x\cos x$  

Find the derivative of the function above. Leave answer in simplest form.

•  $y'=\cos x+\sin x$  

•  $y'=\sin x^2$  

•  $y'=\cos x+x\sin x-\cos x$  

•  $y'=x\sin x$  

 $y=\sec^2x-\tan^2x$  

Find the derivative of the function above. Leave answer in simplest form.

• Wow this is really messy

•  $y'=\sec x\sec x\tan x-2\tan x\sec^2x$  

•  $y'=\sec^2x\tan^2x-\sec^4x$  

• The correct answer is not listed.