Question

Math

Posted 4 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

Verified answer

Posted 4 months ago

Solution by Steps

step 1

To find the slope of the tangent line to the curve at a specific point, we need to calculate the derivative of the function

step 2

The derivative of the function $y = 3x^2 - 2x + 1$ is found using the power rule

step 3

Applying the power rule, the derivative is $\frac{dy}{dx} = 6x - 2$

step 4

To find the slope at $x = 1$, we substitute $x = 1$ into the derivative

step 5

Substituting $x = 1$ gives us $\frac{dy}{dx} = 6(1) - 2 = 4$

Answer

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

Key Concept

Derivative as Slope of Tangent

Explanation

The derivative of a function at a point gives the slope of the tangent line to the curve at that point.

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