Question

Let f(x) be a differentiable function such that f(3) = 15, f(6) = 3. What is f'(x) at x = 3?

a) 5
b) -5
c) 4
d) -4

Answer 1

With only two points provided and without the function's rule or additional information about its behavior, it is impossible to determine the derivative f'(x) at x = 3.

Step-by-step explanation:

The original question asks to find the value of f'(x) at x = 3 for a differentiable function f(x) where it is known that f(3) = 15 and f(6) = 3. This question gives two points on the function and implicitly asks to either use the definition of the derivative (if one exists) or to apply some principle or rule to determine the slope at x = 3. However, without a given function or more information on how f(x) behaves between x = 3 and x = 6, it is impossible to determine the exact value of f'(3).

Therefore, with the information provided, the derivative of the function at x = 3 cannot be calculated. It is important to remember that a derivative represents the instantaneous rate of change of a function at a particular point, and to calculate it, one must know the function's rule or have enough information to use the difference quotient limit definition.