For the function f(x) = x^2 - 4x + 3, what is the slope of the tangent line at x = 3?
Show the answer and explanation
Correct answer
B. 2
Principle or equation
The derivative f'(x) gives the slope of the tangent line at any point x. For a quadratic, f'(x) = 2x + b if f(x) = ax^2 + bx + c.
Why this answer is correct
Compute f'(x) = 2x - 4. At x = 3, f'(3) = 2(3) - 4 = 2. Thus the slope is 2.
Example
For f(x) = x^2, f'(x) = 2x, so at x = 5 the tangent slope is 10.
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