What is the equation of the line tangent

Angelina Proctor

Angelina Proctor

Answered question

2022-04-10

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

Answer & Explanation

Egerlandsq0z

Egerlandsq0z

Beginner2022-04-11Added 14 answers

f(x)=x3
f(x)=3x2
Equation of a straight line with slope m and intercept on the y-axis c is given by:
y=mx+c
In this question we are asked to find the line tangent to f(x) at x=1
Slope of f(x) at x=1 is f(1)=3.12=3m=3
Since f(1)=1 we know that the tangent line passes through the point (1,1)
Hence substituting for x, y and m in the equation above:
1=3.1+c
c=-2
The tangent line is therefore y=3x-2

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