Question

Find the equation of the normal to the curve y=x²+4x-3 at point(1,2)

273

likes

1367 views

Answer to a math question Find the equation of the normal to the curve y=x²+4x-3 at point(1,2)

$Expert avatar$

Maude

4.7

107 Answers

First, find the derivative of the curve to get the slope of the tangent line. y = x² + 4x - 3 y' = 2x + 4 Evaluate the derivative at the point (1, 2) to find the slope of the tangent line at that point. y'(1) = 2(1) + 4 = 2 + 4 = 6 So, the slope of the tangent line at (1, 2) is 6. The slope of the normal line will be the negative reciprocal of the slope of the tangent line. Therefore, the slope of the normal line is -1/6. Now that you have the slope of the normal line and the point (1, 2), you can use the point-slope form of a line to find the equation of the normal line: y - y₁ = m(x - x₁) Where: (x₁, y₁) = (1, 2) m = -1/6 (slope of the normal line) Now, plug in the values: y - 2 = (-1/6)(x - 1) Multiply both sides by 6 to eliminate the fraction: 6(y - 2) = -1(x - 1) 6y - 12 = -x + 1 Now, rearrange the equation to get it in standard form: x + 6y = 13

Frequently asked questions (FAQs)

Find the roots of the cubic equation x^3 - 4x^2 + 3x + 1 = 0.

What is the area of a triangle with side lengths 5, 12, and 13 according to Heron's Formula?

Question: What is the derivative of ∫(3x^2 - 4x + 1) dx using the Fundamental Theorem of Calculus?

New questions in Mathematics

How to find the value of x and y which satisfy both equations x-2y=24 and 8x-y=117

Convert the following function from standard form to vertex form f(x) = x^2 + 7x - 1

The sum of an infinite geometric series is 13,5 The sum of the same series, calculated from the third term is 1,5. Q. Calculate r if r>0.

A book is between 400 and 450 pages. If we count them 2 at a time there is none left over, if we count them 5 at a time there is none left over and if we count them 7 at a time there are none left over, how many pages does the book have?

two particles start at the origin and move along the x axis. for 0 <= t <= 10, their respective position functions are given by x1 = cos(t) and x2 = (e^-3t) + 1. for how many values of t do the particles have the same velocity?

The derivative of a power is obtained just by subtracting 1 from the power True or false

Given that y = ×(2x + 1)*, show that dy = (2x + 1)" (Ax + B) dx where n, A and B are constants to be found.