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Find the slope of the tangent to the curve

y = 3x^2 - 2x + 1

x = 1

Apr 22, 2024

Find the slope of the tangent to the curve

y = 3x^2 - 2x + 1

x = 1

Generated Graph

Solution by Steps

step 1

To find the slope of the tangent line to the curve

y = 3x^2 - 2x + 1

at a specific point, we need to compute the derivative of

y

with respect to

x

step 2

The derivative of

y

with respect to

x

y' = \frac{dy}{dx} = 6x - 2

step 3

To find the slope at

x = 1

, we substitute

1

into the derivative:

y'(1) = 6(1) - 2

step 4

Simplifying gives us the slope at

x = 1

y'(1) = 6 - 2 = 4

Answer

The slope of the tangent to the curve at

x = 1

4

Key Concept

Finding the slope of a tangent line at a point

Explanation

The slope of the tangent line to a curve at a given point is the value of the derivative of the curve's equation evaluated at that point.