How do you find the equation of the

Angela Harrell

Angela Harrell

Answered question

2022-04-15

How do you find the equation of the line tangent to f(x)=x3 at x=2?

Answer & Explanation

seskew192atp

seskew192atp

Beginner2022-04-16Added 12 answers

f(2)=23=8 and hence (2,8) lies on the curve and the tangent.
The gradient (slope) of the tangent at any point is represented by the derivative at that point.
f(x)=3x2
f(2)=3×22=12.
The tangent is a straight line so has linear equation y=mx+c.
Substituting the point (2,8) in this equation, we get :
8=(12)(2)+c
c=16.
Hence the equation of the required tangent line to the curve is
y=2x-16

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