Questions from General Calculus

Q: If f has a local minimum value at c, show that

If f has a local minimum value at c, show that the function g(x) = -f (x) has a local maximum value at c.

Q: The volume of a cube is increasing at a rate of 10

The volume of a cube is increasing at a rate of 10 cm3/min. How fast is the surface area increasing when the length of an edge is 30 cm?

Q: Find the absolute maximum and absolute minimum values of f on the

Find the absolute maximum and absolute minimum values of f on the given interval. f (x) = x3 - 6x2 + 5, [-3, 5]

Q: Find the absolute maximum and absolute minimum values of f on the

Find the absolute maximum and absolute minimum values of f on the given interval. f (x) = 3x4 - 4x3 - 12x2 + 1, [-2, 3]

Q: Find the absolute maximum and absolute minimum values of f on the

Find the absolute maximum and absolute minimum values of f on the given interval. f (t) = (t2 - 4)3, [-2, 3]

Q: Find the derivative of the function. Simplify where possible.

Find the derivative of the function. Simplify where possible. F(x) = x sec-1(x3)

Q: Find the absolute maximum and absolute minimum values of f on the

Find the absolute maximum and absolute minimum values of f on the given interval. f (t) = 2cos t + sin 2t, [0, π/2]

Q: Find the absolute maximum and absolute minimum values of f on the

Find the absolute maximum and absolute minimum values of f on the given interval. f (t) = t + cot (t/2), [π/4, 7π/4]

Q: A paper cup has the shape of a cone with height 10

A paper cup has the shape of a cone with height 10 cm and radius 3 cm (at the top). If water is poured into the cup at a rate of 2 cm3/s, how fast is the water level rising when the water is 5 cm deep...

Q: Find the absolute maximum and absolute minimum values of f on the

Find the absolute maximum and absolute minimum values of f on the given interval. f (x) = x-2 ln x , [1/2, 4]