Calculus Help & Past Papers
The function f, whose graph is shown above, is defined on the interval -2 ≤ x ≤ 2. Which of the following statements about f is false?
(A) f is continuous at x = 0.
(B) f is differentiable at x = 0.
(C) f has a critical point at x = 0.
(D) f has an absolute minimum at x = 0.
(E) The concavity of the graph of f changes at x = 0.
Let f and g be the functions given by f(x) = ex and g(x) = x4. On what intervals is the rate of change of f(x) greater than the rate of change of g(x)) ?
The graph of the piecewise linear function f is shown above.
Let f be a function having derivatives of all orders for x > 0 such that f(3)= 2, f'(3) = 1, f''(3) = 6, and f'''(3) = 12. Which of the following is the third-degree Taylor polynomial for f about x = 3 ?
The graph of f', the derivative of the function f, is shown above. Which of the following statements must be true?
Let f be a function that is twice differentiable on -2 < x < 2 and satisfies the conditions in the table above. If f(x) = f(-x) , what are the x-coordinates of the points of inflection of the graph of f on -2 < x < 2?
What is the average value of y = √cos x on the interval 0 ≤ x ≤ π/2?
If the function f is continuous at x = 3, which of the following must be true?
For -1.5 < x < 1.5, let f be a function with first derivative given by f'(x) = e(x4 - 2x2 + 1) - 2. Which of the following are all intervals on which the graph of f is concave down?
The fuel consumption of a car, in miles per gallon (mpg), is modeled by where s is the speed of the car, in miles per hour. If the car is traveling at 50 miles per hour and its speed is changing at the rate of 20 miles / hour2 , what is the rate at which its fuel consumption is changing?
If f'(x) > 0 for all real numbers x
Let R be the region in the first quadrant bounded above by the graph of y = ln(3 - x) for 0 < x < 2. R is the base of a solid for which each cross section perpendicular to the x-axis is a square. What is the volume of the solid?
The derivative of a function f is increasing for x < 0 and decreasing for x > 0. Which of the following could be the graph of f?
A particle moves along a line so that its acceleration for t ≥ 0 is given by
If the series
The figure above shows the graphs of the polar curves r = 2cos 3θ and r = 2. What is the sum of the areas of the shaded regions?
The function h is differentiable, and for all values of x, h(x) = h(x - 2). Which of the following statements must be true?
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.