2. Find the derivative of f (x) = 5x + 9 at x = 2. A) 9 B) 5 C) 0 D) 10 f (x) = 5x + 9 The first thing we should do in this case is to derive the function. We have then: f '(x) = 5 We now evaluate the function for the value of x = 2. We have then: f '(2) = 5 Answer: the derivative of f (x) = 5x + 9 at x = 2 is: B) 5
3. Find the derivative of f (x) = 8 divided by x at x = -1.
4 0 8 -8
f (x) = 8 / x The first thing we should do in this case is to derive the function. We have then: f '(x) = ((0 * x) - (1 * 8)) / (x ^ 2) Rewriting we have: f '(x) = -8 / (x ^ 2) We now evaluate the function for the value of x = -1. We have then: f '(- 1) = -8 / ((- 1) ^ 2) f '(- 1) = -8 Answer: The derivative of f (x) = 8 divided by x at x = -1 is: -8
4. Find the derivative of f (x) = negative 11 divided by x at x = 9. A) 11 divided by 9 B) 81 divided by 11 C) 9 divided by 11 D) 11 divided by 81
f (x) = -11 / x The first thing we should do in this case is to derive the function. We have then: f '(x) = ((0 * x) - (1 * (- 11))) / (x ^ 2) Rewriting we have: f '(x) = 11 / (x ^ 2) We now evaluate the function for the value of x = 9. We have then: f '(9) = 11 / ((9) ^ 2) f '(9) = 11/81 Answer: the derivative of f (x) = negative 11 divided by x at x = 9 is: D) 11 divided by 81
5. The position of an object at time is given by s (t) = 3 - 4t. Find the instantaneous velocity at t = 8 by finding the derivative. s (t) = 3 - 4t For this case, the first thing we must do is derive the given expression. We have then: s' (t) = - 4 We evaluate now for t = 8 s' (8) = - 4 Answer: the instantaneous velocity at t = 8 by finding the derivative is: s' (8) = - 4
