Please check work on derivatives lab

[tjohn101]

Homework Statement

Sorry about not using the template, but I didn't really see how I could have. If you guys/gals could please check over my answers to these questions and point out the ones I miss that would be outstanding. Thank you!

1. The position of an object moving on a coordinate line is given by s=t² −7t+10, were s is in meters
and t is in seconds. When, if ever, during the interval 0≤ t ≤7 does the object change directions?
Answer: at t = 3.5 sec

2. At time t, the position of an object moving along the s axis is s=t³−15t²+78t were s is in meters
and t is in seconds. Find the total distance traveled by the object from t = 0 to t = 3 .
Answer: 126 m

3. Suppose that the cost of producing x radios is given by C(x)=800+40x−0.2x² . Find the cost per radio of producing the first 30 radios.
Answer: $60.67

4. Find the line tangent to the graph of f (x) =cosx at x = pi/2 .
Answer: y =1

5. Find the 34th derivative of f (x) = cosx.
Answer: f 34(x) = −cosx

6. g(x)=(cscx+cotx)(cscx−cotx) , find g'(x) .
C. g'(x) = − csc2x <-----not sure about this one.

7. f (x)= sqrt(11x−x⁵) , find f '(x) .
Answer: 1 - (2sqrt(11x-x⁵))

8. g(x)=sec5(x2−2x), find g'(x) .
Answer: 5⋅sec⁴(x²−2x)tan (x²−2x) <----Really not sure about this one

9. Find the equation of the line tangent to the graph of f(x) = x3 x3+3 at x =1.
Answer: y=27/4x-13/4

10. The total revenue from the sale of x stereos is given by
R(x) = 2000(1 - x/600)². Find the marginal
revenue, if necessary round to the nearest thousandth.
Answer: R'(x)= 4000(1 - x/600)

 

[mmmboh]

I didn't check all of them, 1 is right, 2 I believe is right, I think 4 is -1, 5 is right, 7 is wrong, the answer should be $$\frac{11-5x^4}{2\sqrt[2]{(11x-x^5)}}$$.You should use http://www.wolframalpha.com/" to check your answers, just type in dervive "your equation" and it will show you the answer and steps.