What is the equation of the tangent line

Jaylen Cantrell

Jaylen Cantrell

Answered question

2022-04-10

What is the equation of the tangent line of f(x)=(x1)(3x3ex21) at x=1?

Answer & Explanation

ze2m1ingkdvu

ze2m1ingkdvu

Beginner2022-04-11Added 16 answers

For the given function f(1)=0. So, the tangent line that we want goes through (1,0) and has a slope given by f'(1).
To find the derivative of f(x) quickly, note that according to the formula
ddx(uv)=udvdx+vdudx, we do not need to differentiate the second factor of our
expression - since that will be multiplied by (x-1) and hence will vanish at x=1.
So
f(1)=1×(3×13×exp(121))=33=0
Thus the tangent is y=0 - the x axis.

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