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 first need to find the derivative of the function

step 2

The derivative of $y = 3x^2 - 2x + 1$ is $y' = \frac{d}{dx}(3x^2 - 2x + 1)$

step 3

Using the power rule, we get $y' = 6x - 2$

step 4

Now, we evaluate the derivative at $x = 1$: $y'(1) = 6(1) - 2 = 4$

step 5

Therefore, the slope of the tangent line to the curve at $x = 1$ is $4$

Answer

The slope of the tangent line to the curve $y = 3x^2 - 2x + 1$ at $x = 1$ is $4$.

Key Concept

Derivative

Explanation

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

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