Questions from General Calculus

Q: Suppose that f is continuous on [0, 4], f

Suppose that f is continuous on [0, 4], f (0) = 1, and 2 ≤ f ‘(x) ≤ 5 for all x in (0, 4). Show that 9 ≤ f (4) ≤ 21.

Q: (a) The volume of a growing spherical cell is V

(a) The volume of a growing spherical cell is V = 4/3 πr3, where the radius r is measured in micrometers (1 μm − 1026 m). Find the average rate of change of V with respect to r when r changes from (i)...

Q: By applying the Mean Value Theorem to the function f (x

By applying the Mean Value Theorem to the function f (x) = x1/5 on the interval [32, 33], show that 2 < 5 33 < 2.0125

Q: For what values of the constants a and b is (1

For what values of the constants a and b is (1, 3) a point of inflection of the curve y = ax3 + bx2?

Q: Let g(x) = f (x2), where f

Let g(x) = f (x2), where f is twice differentiable for all x, f ‘(x) > 0 for all x ≠ 0, and f is concave downward on (-∞, 0) and concave upward on (0, ∞). (a) At what numbers does g have an extreme va...

Q: Sketch the graph of a function that satisfies the given conditions.

Sketch the graph of a function that satisfies the given conditions. f is odd, f ‘(x)

Q: Find two positive integers such that the sum of the first number

Find two positive integers such that the sum of the first number and four times the second number is 1000 and the product of the numbers is as large as possible.

Q: Find the point on the hyperbola xy = 8 that is closest

Find the point on the hyperbola xy = 8 that is closest to the point (3, 0).

Q: Find the smallest possible area of an isosceles triangle that is circumscribed

Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius r.

Q: Find the volume of the largest circular cone that can be inscribed

Find the volume of the largest circular cone that can be inscribed in a sphere of radius r.