What is the equation of the tangent line

Kasey Castillo

Kasey Castillo

Answered question

2022-04-08

What is the equation of the tangent line of f(x)=(9+x)2 at x=6?

Answer & Explanation

aludirao09au

aludirao09au

Beginner2022-04-09Added 11 answers

Explanation:
f(x)=(9+x)2
f'(x)=2(9+x)*1
f'(x)=18+2x
since f'(x) is a gradient of tangent, therefore
when x=6 ot gradient, m=18+2(6)=30
When x=x1=6,f(6)=y1=(9+6)2=225
Therefore,
yy1=m(xx1)
y-225=30(x-6)
y=30x-180+225
y=30x-45

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