need solution with steps

Question 1 1 pts For each of the functions below, select the reason why it is not differentiable at x =0 .y=x1/3 [ Select ] The function has a corner at x=0. The function has a cusp at x=0. . y = exl The function has a vertical tangent at x=0. The function is undefined or discontinuous at x=0. . y = |x/1/3 [ Select ] . y = In |x| [ Select ]Question 2 1 pts If f: R - R is a differentiable function, whose graph never crosses the x-axis, then we can definitely conclude that.. (Choose all that apply.) ... f has no horizontal tangent lines. ).. f has no vertical tangent lines. ... f' never crosses the x-axis. O ... f' must cross the x-axis at least once. O.. f has no points of discontinuity.Question 3 1 pts Here is the graph of the derivative of a continuous function f: R - R . What would we see on the graph of f when x=0 ? f'(x) A corner. O A jump. O A cusp A vertical tangent O A horizontal tangent.Question 4 1 pts In the following question, show all your steps, and do not use any differentiation rules from Section 3.3. Let f (x)=x--+5. x (a) Using the Definition of the Derivative from page 125, determine f '(x). (b) Using the Alternative Formula for the Derivative from page 126, determine f '(x) again (you should get the same answer as in (a) ). Upload Choose a FileQuestion 5 1 pt Which of the following lines is perpendicular to the tangent line of y= X at the point x- 3 (2, -2) ? Oy = -3x +4 X -4 3 X - 4 O X 8 IS 3\fQuestion 7 1 pts The curve y= ax +bx+c passes through the point (1 , 2) . The line y=2x+1 is tangent to the curve when x=0 . What are the values of a , b and c ? O a = 1, b = 2, c=1 O a = 1, b = -2, c=1 O a = -1, b= 2, c=-1 Oa = -1. b= =2, c=1 Oa=-1, b = 2. c=1Question 8 1 pts Assume the functions f and g are differentiable functions, with f(1)=6. f'(1)=-2. g( 1) =-1 and g '(1) = 3. Find an equation of the line perpendicular to the graph of F(x) = f(x) + 3x at x=l. 2 - g(x) Upload Choose a FileQuestion 9 1 pts Consider the effect of gravity on falling objects. If you drop an object, from rest, on earth, it will travel d(1)=4.91- meters in t seconds. How high do you need to lift a ball (in meters), so that it will be traveling at 98 meters per second when it hits the ground? Your answer should be an integer.Question 10 1 pts The volume of a spherical balloon changes with respect to the radius r . At what rate (in fts/ft) does the volume change with respect to the radius when r= 2 ft ? O 32A 3 12Question 11 1 pts The position of an object moving on a number line is given by s(1) =1 +3 . At which of the following instants is the object slowing down? Choose all that apply. 01=-2 1 1= 2Question 12 1 pts Let f(x)=x2-3x+5. Show that the average rate of change of f (with respect to x) on an arbitrary interval [a , b] is equal to the instantaneous rate of change of f at the midpoint of that interval. Show and explain your work. (Note: This will be true for any quadratic function, and not just for the given one.) Upload Choose a File