Hello I need help with these calculus questions, that are down below. For a good review please be detailed and thorough. For the multiple question you can just give me the answer. For the rest of the question please be detailed and thorough. Thank you

Multiple Choice Circle the choice that best completes the statement or answers the question. Also write the letter corresponding to your choice on the appropriate line. 1. Determine f'(2) for A(x) = x2 +4x - 1. a. 7 C. 11 b. 8 d. 12 2. All but one of the functions is differentiable for all real values of x. Which function is not differentiable for at least one real value of x? a. A(x) = x+1 c. h(x) = \\x| b. g(x) = - d. j(x) = x - 3x x2 + 1 3. Determine the derivative for y = 2x - 3x + 1. a. 6x2- 3 C. 3x2 - 3 b. 6x2 - 3x d. x2 - 3 dy for y = * x - 4 4. Determine - f x2 + 4 when x = 1. a. 10 C. 16 25 25 b. 4 d. 1 25 5. The position s, in metres, of an object moving in a straight line is given by s(1) = 5t(t-2) , where t is the time in seconds. Determine the velocity of the object at time t = 1. a. 15 m/s 0 m/s b. 5 m/s . -5 m/s 6. An initial population, p, of 1500 bacteria grows in number according to the equation p() = 1500|1+ - 5t 12 + 30 where t is in hours. Determine the rate at which the population is growing after 3 h. a. 0.069 bacteria/h C. 281 bacteria/h b. 104 bacteria/h d. 4038 bacteria/h 7. For which value(s) of x is the tangent to f(x) = * + 3 x + 1 horizontal? x=1 C. x= -1, 3 x = -3, 1 d. x=3 8. Determine the value of k for which f'(3) = 2, if A(x) = + * x- 1 a. C. 5 b. -5 d. 99. If A(x) = ~x-1 and g(x) = x+ 1, which expression is equal to fig(x))? a. 1+ x2 - 1 c. (x + 1)2 - 1 b. ~x2 + 2x d. ~x2 + x - 1 10. Determine the slope of the tangent to the curve y = (2x - 3x ) at (1, 1). a. -16 -2 b. -8 d. 8 Full Solutions: 11. a. Use the formal definition of the derivative to determine f' (x) for A(x) = /x-1. b. Determine the slope of the tangent to f(x) at (10, 3). 12. Determine the values of a, b, and c for f(x) = ax + bx + c so that /'(x) = 6x - 3 and f(2) = -1. 13. The population of a rabbits in a controlled system can be described by P(x) = -x* + 18x + 19, where x is the number of years after the population was first tracked. a. What is the meaning of P'(x) for this scenario? b. P'(11) = -4. Explain what this means 14. a. Determine the derivative of A(x) = (x + 1) (3x -5)* . Write your answer in simplified factored form. b. Determine the value(s) of x for which the graph of f(x) has a horizontal tangent. 15. a. Determine the point (a, f(a)) for which f'(a) = a, given that f(x) = -x2 + 3x - 7. b. Write the equation of the tangent to f(x) at the point found in part a. 16. a. Determine f'(x) if A(x) = (8x* + x) . Write your answer in simplified form. b. Determine 17. a. Determine x dy ify = ( 3x 2 + 2 ) 3 Write your answer in simplified form. b. State any values of x for which the function is not differentiable. (x + 2)3 18. a. Differentiate A(x) = (x + 3)(2x - 1) . Simplify your answer. b. State which rules of differentiation you used