This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hey asanda, good to see you again. To determine the derivative of f(x) = 3x - 1 from first principles, we use the definition: f'(x) = _h 0 (f(x+h) - f(x))/(h) Step 1: Find f(x+h). Substitute x+h into the function f(x): f(x+h) = 3(x+h) - 1 f(x+h) = 3x + 3h - 1 Step 2: Calculate f(x+h) - f(x). Subtract the original function f(x) from f(x+h): f(x+h) - f(x) = (3x + 3h - 1) - (3x - 1) f(x+h) - f(x) = 3x + 3h - 1 - 3x + 1 f(x+h) - f(x) = 3h Step 3: Substitute into the limit definition and simplify. (f(x+h) - f(x))/(h) = (3h)/(h) (f(x+h) - f(x))/(h) = 3 Step 4: Evaluate the limit. Now, take the limit as h 0: f'(x) = _h 0 3 Since there is no h in the expression, the limit is simply 3. f'(x) = 3 The derivative of f(x) = 3x - 1 from first principles is: 3 Send me the next one 📸