i already tried these problems, however I do not know if they are correct. So it would be very helpful if someone were to double check my answers.

les of Calculus Name bea 43 Derivatives - Graded Assignment Date QUE DATE: Friday 10/15 You may use your notes to answer the following questions. Show all work to receive full credit. If you have questions, you may ONLY see me for help. Make sure to turn this in on the day it is due. if it is late, I will deduct 2 points for every day it is late. 1) The distance a car has traveled on a trip is shown in the table as a function of time since the trip started. (4 points) t (minutes) 0 .5 1.5 2 s (km) 0 1.25 3 5.25 8 a. Find the average velocity between 0 and 1.5 minutes. 13.5 KM 5.25 - 0 5.25- 3, 6 Min 1.5 - 0 7.5 b. Find the average velocity between .5 and 2 minutes. 8 - 1. 25 675 4.5 KM 1-5 1= 4.5 min 2 -.5 2) The information in the previous problem can be modeled with the equation: (6 points) s (t ) = 12 + 2t f ( x + c ) - f ( x ) a. Calculate the derivative function s'(t). ( t + c ) + 2 (*+c ) +/ xact + ( 2 + Xe tac /- HE at +2 to flow= 26 + 2 20 t + $ 2 + 24 _ at + 2 + 0 lim C-O b. What is the instantaneous velocity when the car has traveled 1 minute? 2(1 ) + 2 = 2+2 . = 4 3) Find the derivative of each function using the definition of the derivative: (8 points) a. g ( x ) = - 4 x 3 + 2 = g ( x + c) = - 4 ( x 3 +c,# + 3*?c+. 3xc2)+2? ( x + ( ) ( * + ( ) ( x + c ) g ( x ) =-12x ( x 3 + c B + 3 x 2 C + 3 x ( ?) g " ( x ) = 1 { 5 4 ( x 3 + of + 3 x 2 ( + 3 # c 2 ) + 2 7 - 4 [- 4 x 3 +2] - 4 0- 2 - A x 3 - 4/ 2 - 12 x2 4 - 1 2x 62 +$+ 4x5-2 ex 40 - 2 lim -80 Cao = - 402- 12x2 - 12xc - - 4 (0)2- 12x2-12 x(0D/- d =- 12x2