What is the equation of the tangent line

Santos Mooney

Santos Mooney

Answered question

2022-04-07

What is the equation of the tangent line of f(x)=(x235)7 at x=6?

Answer & Explanation

wyjadaczeqa8

wyjadaczeqa8

Beginner2022-04-08Added 14 answers

Find the point the tangent line will intersect.
f(6)=(6235)7=1
The point is (6,1).
Now, to find the slope of the tangent line, find f'(6).
Finding f'(x) will require the chain rule:
f(x)=7(x235)6ddx[x235]
f(x)=7(x235)6(2x)
f(x)=14x(x235)6
f(6)=14(6)(6235)6=84
Write the equation of the tangent line in point-slope form:
y-1=84(x-6)
In slope-intercept form:
y=84x-503

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