What is the equation of the line normal

Essence Ingram

Essence Ingram

Answered question

2022-04-10

What is the equation of the line normal to f(x)=6x2+4x9 at x=1?

Answer & Explanation

chambasos6

chambasos6

Beginner2022-04-11Added 12 answers

Explanation:
y at x = 1 is 1. So, the foot of the normal is P(1, 1).
y'=12x+4=16, at P.
The slope of the normal =1y=116
So, the equation to the normal at P(1, 1) is
y1=116(x1), giving
x+16y-17=0
Frain4i62

Frain4i62

Beginner2022-04-12Added 16 answers

We are given that f(x)=6x2+4x9 and x0=1
Find the value of the function at the given point: y0=f(1)=1.
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)=(6x2+4x9)=12x+4
Hence, M(x0)=1f(x0)=112x0+4
Next, find the slope at the given point.
m=M(1)=116
Finally, the equation of the normal line is yy0=m(xx0)
Plugging the found values, we get that y1=x116
Or, more simply: y=1716x16.

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