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MATH 16A WORKSHEET 4-
(1) Find all points P on the graph of f(x) = x3 - 4x such that the tangent line to f at P is perpendicular to y = x.
(2) Use limits to compute f'(1), where f(x) = x√x.
(3) Find a function f(x) and a real number a such that f'(a) = limh→0((2 + h)3 - 8/h), and find this limit by computing the derivative f'(x) and evaluating at x = a.
(4) Let f be the function defined as follows:
Draw a graph of f. Determine if f is continuous and/or differentiable at x = 0 and at x = 1.
(5) Compute the derivative of f(x) =1/√(x4+1) at x = 0.
(6) Find the equation of the tangent line to f(x) = 2/√(x-1) at x = 4.
A box contains 4 green, 10 red, 6 yellow, and 5 blue marbles. Four marbles are drawn from the box without replacement. What is the probability that you get one marble of each color?
Calculate the perimeter of the garden and the area of the space covered
Car Insurance . Use the histogram below to answer the following questions: How many students were surveyed? What are the lower and upper class limits of the first and second classes?
Johnny bought some sponges the number of packages he bought was2 less than the number of sponges per package. Johnny bought 35 sponges on all. How many sponges were in each package?
Sketch the graph of the inventory as a function of time t (days). At what times is the graph discontinuous?
State the quadratic formula. Take your example from last week's completing the square, or pick a new quadratic equation, and solve it using the quadratic formula. Example: x^2-18x-4=0
Find the derivative of the function.
Find the volume of the solid generated by revolving the following region about the y-axis. The region in the first quadrant bounded above by the parobola y=x^2, below by the x-axis, and on the right by the line x=3.
two trucks leave the warehouse at the same time. 3 hours later, they are 429 miles apart. If one truck was driving 15 MPH slower than the other, how many miles did each drive?
At what rate is the base of the triangle changing when the altitude is 17 centimeters and the area is 204 square centimeters?
Find the amount of work in foot-pounds required to empty the trough by pumping the water over the top. Note: The weight of water is 62 pounds per cubic foot.
Trina's paycheck earning p, varies directly as the number of hours, h, she works. If she works 19 hours and earns $187.15 what should she earn if she worked 40 Hours
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