Questions from General Calculus

Q: The third derivative of a function f (x) is the

The third derivative of a function f (x) is the derivative of the second derivative f ‘(x) and is denoted by f ‘(x). Compute f ‘(x) for the following functions: (a) f (x) = x5 - x4 + 3x (b) f (x) = 4x...

Q: Compute the third derivatives of the following functions: (a

Compute the third derivatives of the following functions: (a) f (t) = t10 (b) f (z) = 1/z + 5

Q: For the given function, simultaneously graph the functions f (x

For the given function, simultaneously graph the functions f (x), f (x), and f (x) with the specified window setting. f (x) = x/1 + x2 , [-4, 4] by [-2, 2].

Q: Consider the cost function of Example 6. (a)

Consider the cost function of Example 6. (a) Graph C(x) in the window [0, 60] by [-300, 1260]. (b) For what level of production will the cost be $535? (c) For what level of production will the margina...

Q: Find the first derivatives. f (t) = (

Find the first derivatives. f (t) = (t2 + 1)5

Q: Find the first derivatives. f (P) = P3

Find the first derivatives. f (P) = P3 + 3P2 - 7P + 2

Q: Differentiate. y = (x3 + x2 + 1)

Differentiate. y = (x3 + x2 + 1)7

Q: Find the first derivatives. y(t) = 4t2

Find the first derivatives. y(t) = 4t2 + 11 √t + 1

Q: Find the first derivatives. g(y) = y2

Find the first derivatives. g(y) = y2 - 2y + 4

Q: Suppose that f (x) = -6/x.

Suppose that f (x) = -6/x. (a) What is the average rate of change of f (x) over each of the intervals 1 to 2, 1 to 1.5, and 1 to 1.2? (b) What is the (instantaneous) rate of change of f (x) when x = 1...