Derivatives Test

Derivatives Test (No calculator)

Find the appropriate derivative of the following equations. 1. fx=x5-18x2+14x f'x=?

3. hx=2x+12x-1 h'x=?

5. kx=e1+log2x k'x=?

2. gx=2sinxcosx g'x=?

4. y=lnx2 d2ydx2=?

6. y3+y=2tanx dydx=?

7. Find the equation for the tangent line to x2+2y2=9 at the point (1, 2).

8. Find dydx.

y=2cost

x=2sint

9. Find f'(x) for fx=ln⁡(x3+2)

BONUS: Use the graph of f to sketch the graph of f'.

Derivatives Test (Calculator Active) 1. Dorothy emptied a bucket of water on the Wicked Witch of the West,

who immediately began to melt. If the Scarecrow only had a brain, he would calculate that the witch’s height could now be give by the function ht=630.91t where t is measured in seconds since the water was first thrown upon the witch and h(t) is measured in inches. a. At time t = 11 seconds, how tall was the witch? b. How quickly was her height changing? Round your answers to 3 decimal places if needed and include appropriate units.

1. The following graphs show the distance traveled, velocity and

acceleration for each second of a 2-minute car trip. Which graph shows (a) distance? (b) velocity? (c) acceleration? Explain your reasoning .

2. A man lives in a high-rise apartment building. He leans out of his

window and throws a ball upward. Between the time the ball is thrown and the time that it hits the ground, the height of the ball is given by the formula ht=-16t2+96t+160, where t is the number of seconds since the ball is first thrown and h(t) is measured in feet above the ground. a. What is the instantaneous velocity of the ball at t = 1.5 seconds? b. When does the ball reach its maximum height? c. What is the ball’s maximum height? d. When does the ball hit the ground? e. How fast is the ball going when it hits the ground? f. What is the acceleration function for the ball?

BONUS: Find the derivative of y=sin-11-x2

**ddxsin-1x=11-x2