For the function f(x) = x^3 - 4x^2 + 5x - 2, what is the slope of the tangent line at x = 3?
Show the answer and explanation
Correct answer
A. 8
Principle or equation
The slope of the tangent line to f(x) at x = a is f'(a). Use the power rule: d/dx(x^n) = n x^(n-1).
Why this answer is correct
Compute f'(x) = 3x^2 - 8x + 5. Then f'(3) = 3(9) - 8(3) + 5 = 27 - 24 + 5 = 8.
Example
For f(x) = x^2 + 3x, f'(x) = 2x + 3, so at x = 1, slope = 5.
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