Question

For \(y = x^3 - 3x^2 + 2\), slope at \(x=2\):

• A. \(0\)
• B. \(2\)
• C. \(4\)
• D. \(6\)

Hint:

Slope of curve: \[ y=f(x) \] at any point is: \[ \frac{dy}{dx} \] Differentiate first, then substitute the given value of \(x\).

Answer 1

The Correct Option is A

Concept: The slope of a curve at a point is given by: \[ \frac{dy}{dx} \] Thus we differentiate the function and substitute the given value of \(x\).

Step 1: Differentiating the function. Given: \[ y=x^3-3x^2+2 \] Differentiate term-by-term: \[ \frac{dy}{dx} = 3x^2-6x \]

Step 2: Substituting \(x=2\). \[ \frac{dy}{dx}\Big|_{x=2} = 3(2)^2-6(2) \] \[ =12-12 \] \[ =0 \] Final Answer: \[ \boxed{(A)\ 0} \]