Question

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Answer 1

 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