Question

Math

Posted 6 months ago

`Find the slope of the tangent to the curve $y = 3x^2 - 2x + 1$ at $x = 1$.`

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Answer from Sia

Posted 6 months ago

Solution by Steps

step 1

To find the slope of the tangent line to the curve $y = 3x^2 - 2x + 1$ at $x = 1$, we need to compute the derivative of $y$ with respect to $x$

step 2

The derivative of $y$ with respect to $x$ is $\frac{dy}{dx} = 6x - 2$

step 3

Evaluate the derivative at $x = 1$ to find the slope of the tangent line at that point: $\frac{dy}{dx} \bigg|_{x=1} = 6(1) - 2$

step 4

Simplifying gives us the slope: $6 - 2 = 4$

Answer

The slope of the tangent to the curve at $x = 1$ is 4.

Key Concept

Finding the slope of a tangent line to a curve at a given point

Explanation

The slope of the tangent line to a curve at a particular point is found by evaluating the derivative of the curve's equation at that point.

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