What is the equation of the tangent line

Rowan Callahan

Rowan Callahan

Answered question

2022-03-24

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

Answer & Explanation

SofZookywookeoybd

SofZookywookeoybd

Beginner2022-03-25Added 15 answers

We must first differentiate f(x).
The derivative of lnx is 1x
The slope of the tangent at a point x=a on the function f(x) is given by evaluating f'(a).
Hence, the slope of the tangent is 11=1.
The function passes through (1,ln1)=(1,0). Now, we can use point slope form to find the equation of the tangent.
yy1=m(xx1)
y-0=1(x-1)
y=x-1
Thus, the equation of the tangent is y=x-1.

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