What is the equation of the line tangent

Kali Thomas

Kali Thomas

Answered question

2022-04-10

What is the equation of the line tangent to f(x)=2x3+8x at x=1

Answer & Explanation

tempur8x43

tempur8x43

Beginner2022-04-11Added 16 answers

Explanation:
The equation of the tangent line is: y=kx+n
where k=f(x0),x0=1
So, f(x)=(2x3+8x)=6x2+8,
and hence k=f(1)=612+8=14
We have: f(x0)=f(1)=213+81=10 and
y(x0)=kx0+n
10=141+nn=4
Finally, y=14x-4

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