Question

Math

Posted 7 months ago

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

Sign in to unlock the answer

Answer from Sia

Posted 7 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.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Unlock Smarter Learning with AskSia Super!

Join Super, our all-in-one AI solution that can greatly improve your learning efficiency.

30% higher accuracy than GPT-4o

Entire learning journey support

The most student-friendly features

Study Other Question