AskSia

Plus

Find the slope of the tangent to the curve

y = 3x^2 - 2x + 1

x = 1

Feb 4, 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

x = 1

, we need to compute the derivative of

y

with respect to

x

step 2

The derivative of

y

with respect to

x

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

step 3

Evaluating the derivative at

x = 1

gives us

\frac{dy}{dx} = 6(1) - 2 = 4

step 4

Therefore, the slope of the tangent line at

x = 1

is 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.