How do you find the equation of the

Aiyana Ayers

Aiyana Ayers

Answered question

2022-04-16

How do you find the equation of the line tangent to y=x32x at the point (2,4)?

Answer & Explanation

mortaraskxnl

mortaraskxnl

Beginner2022-04-17Added 12 answers

Step 1: Take the Derivative
Using the power rule and sum rule, we see that y=3x22.
Step 2: Evaluate to find the Slope
We are looking for the equation of the tangent line, and one component of that is the slope. Since the slope is the derivative at the point, we can evaluate our derivative at x=2 to find the slope:
y=3(2)22
y'=10
Step 3: Finding the Equation
Now that we have the slope (10) and a point (2,4), we can find the equation. Tangent lines are of the form y=mx+b, where x and y are points on the line, m is the slope, and b is the y-intercept. All we are missing is the y-intercept, so that's what we'll solve for:
y=mx+b
4=10(2)+b
4=20+b
b=-16
Putting all the information together, the equation of the tangent line at (2,4) is
y=10x-16.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?