Questions from General Calculus

Q: Find dy/dx and d2y/dx2. For which values

Find dy/dx and d2y/dx2. For which values of is the parametric curve concave upward?

Q: In the theory of relativity, the mass of a particle is

In the theory of relativity, the mass of a particle is where m0 is the rest mass of the particle m, is the mass when the particle moves with speed relative to the observer, and c is the speed of light...

Q: A particle moves along the curve y = √1 + x2

A particle moves along the curve y = √1 + x2. As it reaches the point (2, 3), the y-coordinate is increasing at a rate of 4cm/s. How fast is the x-coordinate of the point changing at that instant?

Q: In the theory of relativity, the energy of a particle is

In the theory of relativity, the energy of a particle is where m0 is the rest mass of the particle, is its wave length, and h is Planck’s constant. Sketch the graph of E as a functio...

Q: Find the local maximum and minimum values of using both the First

Find the local maximum and minimum values of using both the First and Second Derivative Tests. Which method do you prefer?

Q: Find a cubic function f (x) = ax3 + bx2

Find a cubic function f (x) = ax3 + bx2 + cx + d that has a local maximum value of 3 at = -2 and a local minimum value of 0 at x= 1.

Q: For what values of the numbers and does the function have the

For what values of the numbers and does the function have the maximum value f (2) = 1?

Q: Show that tan x > x for 0 < x < π

Show that tan x > x for 0 < x < π/2. [ Show that f (x) = tan x - x is increasing on (0, π/2).]

Q: Show that the curve y = (1 + x)/ (

Show that the curve y = (1 + x)/ (1 + x2) has three points of inflection and they all lie on one straight line.

Q: Suppose f" is continuous on (-∞, ∞). (a).

Suppose f" is continuous on (-∞, ∞). (a). If f'(2) = 0 and f"(2) = -5, what can you say about f? (b). If f'(6) = 0 and f"(6) = 0, what can you say about f?