What is the slope of the tangent line to the curve y = x^3 - 3x^2 + 2 at the point where x = 3?
Answer and explanation
Correct answer: B. 9
- Step 1: The slope of the tangent line is given by the derivative dy/dx evaluated at x = 3.
- Step 2: Differentiate y with respect to x: dy/dx = 3x^2 - 6x.
- Step 3: Substitute x = 3: dy/dx |_(x=3) = 3(3)^2 - 6(3) = 3(9) - 18 = 27 - 18 = 9.
Answer
9.
Why not the others: '0' corresponds to critical points at x = 0 and x = 2; '6' makes an arithmetic error during subtraction; '18' subtracts incorrectly from 36.
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