need help in my calculus problems. Thank you !

2. [9 points] This problem concerns the implicit curve I tryty' = 10. a. [5 points] Using implicit differentiation, find the derivative # for the function implicitly defined by the curve. Answer: dy b. [4 points] Find the a- and y- coordinates of all points on the curve where the tangent line is vertical. Answer: (r. y) =3. [14 points] Consider the information about the function h(t) given in the table below. You may assume that h(t) is twice differentiable, invertible. and has continuous first derivative. Moreover, h"(t) is always increasing or decreasing between successive values. 0 1 2 3 h ( t ) - 2 2 3 4 8 h' (t ) 3.5 0.5 2.5 1.5 5 h" (t ) 6 0.25 0.3 -0.4 0.6 In the following questions write the answer on the blank provided. If there is not enough information given to answer the question write "NEI" . Be sure to show your work where appropriate. a. [3 points] Let a(x) = h(x)h'(x). Find a'(1). Answer: a'(1) = b. [4 points] Suppose b(t) = In(1 + h'(t)). Find b'(2). Answer: b' (1) = c. [3 points] Suppose c(t) = h-1(t). Find c(4). Answer: C(4) = d. [4 points] Suppose d(t) = (h-!)'(t). Find d' (0). Answer: d'(0) =4. [12 points] Consider the graph of the function f(t) given below. You may assume that f (t) close attention. is parabolic on [-2. 0). The questions below will reference both f(t) and g(t) = f'(t), so pay y = f (t) -2 -1-10 1 2 3 4 5 In the following questions write the answer on the blank provided. If there is not enough information given to answer the question write "NEI". If the answer does not exist, write "DNE". Be sure to show your work where appropriate. a. [3 points] Suppose a(t) = In(1 + f(t)). Find a'(2). Answer: a'(2) = b. [2 points] Find g'(-2). Answer: g'(-2) = c. [2 points] Find ef(0). Answer: ef(0) = d. [2 points] Find g(0). Answer: g(0) = e. [3 points] Compute lim es(t). t -+ 0+ Answer: lim es(0) = 1-0+5. [8 points] Let B.r if r 1 where B, and C are constants. Find values of B, and C such that S(x) is differentiable.1. [1 1 points] On the axes provided below, sketch the graph of one possible function y = f'(r) - note, your graph should be a sketch of the derivative function. Your functions should satisfy all the following requirements. Your graph should clearly show the properties listed below to receive full credit. . The domain of f'(x) is the interval -6