What is the equation of the line that

Raven Gardner

Raven Gardner

Answered question

2022-04-10

What is the equation of the line that is normal to f(x)=cosxsin2x at x=4π3?

Answer & Explanation

tralhavahr9c

tralhavahr9c

Beginner2022-04-11Added 16 answers

Explanation:
The normal line is perpendicular to the slope at that point, so we have to derive the formula, plug in x=4π3 to find the slope at that point, find the negative reciprocal of the point to get the perpendicular slope, then use y=mx+b to find the y-intercept of the line
f(x)=ddx[cos(x)sin(2x)]=sin(x)2cos(x)
Plug in x=4π3 to get the slope at this point is (3+22), but to find the perpendicular slope you use the negative reciprocal of that slope, which is
23+2
Now with the slope and the point it must intersect (4π3,1+32), find the y-intercept by using y=mx=b to get that messy equation in the answer box.

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