What is the equation of the normal line

Marshall Wolf

Marshall Wolf

Answered question

2022-04-08

What is the equation of the normal line of f(x)=5x3+x25x2 at x=2?

Answer & Explanation

mortaraskxnl

mortaraskxnl

Beginner2022-04-09Added 12 answers

f(x)=5x3+x25x2
At x=2, we have y=f(2)=44-12=32
f(x)=15x2+2x5, so the slope of the tangent line is f'(2)=64-5=59
The normal line is perpendicular to the tangent, so its slope is 159
An equation for the normal line is y=32159(x2).
This can also be written y=159x+32259

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