What is the equation of the tangent line

Alexander Beard

Alexander Beard

Answered question

2022-03-16

What is the equation of the tangent line of y=(x23x)2 at x=-1?

Answer & Explanation

rywleob8

rywleob8

Beginner2022-03-17Added 4 answers

Explanation:
According to the chain rule,
y=2(x23x)21ddx[x23x]
y=2(x23x)(2x3)
y'=2x(x-3)(2x-3)
Finding y'(-1) will give us the slope of the tangent line when x=-1.
y'(-1)=2(-1)(-1-3)(2(-1)-3)=-2(-4)(-5)=-40
Since y(-1)=16, the tangent line will intersect the point (-1, 16).
Write the equation of the line in point-slope form:
y-16=-40(x+1)

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