Find the slope of the tangent to the curve `y=3x^(2)-4x` at the point, whose x - co - ordinate is 2.

Answer

To find the slope of the tangent to the curve \( y = 3x^2 - 4x \) at the point where the x-coordinate is 2, we will follow these steps:

### Step 1: Differentiate the function
We start by differentiating the function \( y \) with respect to \( x \) to find the derivative \( \frac{dy}{dx} \), which represents the slope of the tangent line.

\[ y = 3x^2 - 4x \]

Differentiating term by term:

- The derivative of \( 3x^2 \) is \( 6x \) (using the power rule).
- The derivative of \( -4x \) is \( -4 \).

Thus, we have:

\[ \frac{dy}{dx} = 6x - 4 \]

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

\[ \frac{dy}{dx} \bigg|_{x=2} = 6(2) - 4 \]

Calculating this gives:

\[ \frac{dy}{dx} \bigg|_{x=2} = 12 - 4 = 8 \]

### Conclusion
The slope of the tangent to the curve \( y = 3x^2 - 4x \) at the point where the x-coordinate is 2 is \( 8 \).

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