What is the equation of the line normal

Terrence Riddle

Terrence Riddle

Answered question

2022-04-10

What is the equation of the line normal to f(x)=2x3x2x at x=4?

Answer & Explanation

legaldaj1dn

legaldaj1dn

Beginner2022-04-11Added 9 answers

f(4)=2*64-16-4=128-20=108
f(x)=6x22x1
f'(4)=6*16-8-1=96-9=87
R(x)=187x+b is the desired perp.
R(4)=108487+b=108
b=108+487
abangan85s0

abangan85s0

Beginner2022-04-12Added 16 answers

f(x)=2x3x2x and x0=4.
Find the value of the function at the given point: y0=f(4)=108.
The slope of the normal line at x=x0 is the negative reciprocal of the derivative of the function, evaluated at x=x0:M(x0)=1f(x0)
Find the derivative: f(x)=(2x3x2x)=6x22x1
Hence, M(x0)=1f(x0)=16x022x01
Next, find the slope at the given point.
m=M(4)=187
Finally, the equation of the normal line is yy0=m(xx0)
Plugging the found values, we get that y108=x487
Or, more simply: y=940087x87.

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?