What is the equation of the tangent line

ds522stlk

ds522stlk

Answered question

2022-04-09

What is the equation of the tangent line of f(x)=2x3+6x2+2x3 at x=3?

Answer & Explanation

Mey9ci0

Mey9ci0

Beginner2022-04-10Added 14 answers

Explanation:
The equation of the line is y - b = m (x - a ) where m is gradient
and (a , b ) a point on the line.
To find m (gradient ) we differentiate f(x) as f'(x) gives the gradient of the tangent to the curve.
f(x)=6x2+12x+2
and m=f(3)=6(3)2+12(3)+2=54+36+2=16
a=3:b=f(3)=2(3)3+6(3)2+2(3)3
=-54+54+6-3=3
equation of tangent: y-b=m(x-a), m=-16, (a,b)=(3,3)
so y-3=-16(x-3) hence y-3=-16x+48
y=16x+51

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