How do you find the equation of the tangent line

Beausepoomoubor2

Beausepoomoubor2

Answered question

2022-02-12

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

Answer & Explanation

maskorfclp

maskorfclp

Beginner2022-02-13Added 12 answers

The derivative gives us the general (that is, in terms of x) slope of the line
Given
f(x)=x3
df(x)dx=3x2
At x=2
the slope is m=3(22)=12
-and f(2)=23=8(x,y)=(2,8)
We can use the slope-point form of the line to write:
y-8=12(x-2)
or, in standard form:
12x-y=16

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