The slope of the curve `y = x^(3) - 2x+1` at point x = 1 is equal to :

Options

A. 0
B. 1
C. 2
D. 3

Explanation

To find the slope of the curve \( y = x^3 - 2x + 1 \) at the point \( x = 1 \), we need to follow these steps:

### Step 1: Differentiate the function
We start by finding the derivative of the function \( y \) with respect to \( x \). The derivative \( \frac{dy}{dx} \) gives us the slope of the curve at any point \( x \).

The function is:
\[ y = x^3 - 2x + 1 \]

Now, we differentiate:
\[ \frac{dy}{dx} = \frac{d}{dx}(x^3) - \frac{d}{dx}(2x) + \frac{d}{dx}(1) \]

Calculating each term:
- The derivative of \( x^3 \) is \( 3x^2 \).
- The derivative of \( -2x \) is \( -2 \).
- The derivative of a constant (1) is \( 0 \).

So, we have:
\[ \frac{dy}{dx} = 3x^2 - 2 \]

### Step 2: Substitute \( x = 1 \)
Next, we substitute \( x = 1 \) into the derivative to find the slope at that specific point.

\[ \frac{dy}{dx} \bigg|_{x=1} = 3(1)^2 - 2 \]

Calculating this:
\[ \frac{dy}{dx} \bigg|_{x=1} = 3(1) - 2 = 3 - 2 = 1 \]

### Conclusion
The slope of the curve \( y = x^3 - 2x + 1 \) at the point \( x = 1 \) is \( 1 \).

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