BC Unit 8 Review

Find the average value of $$h\left(x\right)=3x^2-6x+1$$  on [-2,1].

Find the average value of $$g\left(x\right)=5\pi\cos x$$  on the interval  $$\left[0,\frac{\pi}{2}\right]$$ .

Find the average value of the function $$g\left(x\right)=\frac{3}{2x}$$  from x=1 to x=e.

Find the average rate of change of g(x) on the interval $$\left[1,e\right]$$   given $$g"\left(x\right)=\frac{1}{x^2}$$  and $$g'\left(2\right)=0$$  

A particle is moving along the x-axis for $$t\ge0$$  . The position of the particle is given by $$x\left(t\right)=t^3-9t^2-21t+6$$ .  At what time, t, does the particle change direction?

The velocity of a particle for t on [0,9] is given in the graph. At which of the following value for t is the particle speeding up?

A particle is moving along the x-axis. The position and velocity of the particle is recorded for various times in the table. At which time, t, is the particle moving towards the origin?

The velocity of a particle is given in the graph for t on [0,11]. What is the total distance traveled by the particle on the interval [4,9]?

The position of a bug moving along a straight path is given by $$s\left(t\right)=t^2-2t+3$$  .  At what time, t, is the instantaneous velocity equal to the average velocity of the bug on [0,6]?

Snow is falling at a rate of $$r\left(t\right)=2e^{-0.1t}$$  inches per hour, where t is the time in hours since the beginning of the snowfall.  There initially was 5 inches of snow on the ground. Which of the following gives the amount of snow, in inches, that falls from time t=0 to t=5 hours?