Find the equation of the tangent line to f(x)=(x-1)5 at the point where x=2.

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15-01-2018
Mathematics

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Find the equation of the tangent line to f(x)=(x-1)5 at the point where x=2.

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Rod44 Rod44 · Answer 1 · 2018-01-15T16:09:23+01:00

Rod44 Rod44

15-01-2018

f(x)=(x-1)⁵, f'(x)=5(x-1)⁴. When x=2, f'(x)=5 the gradient of the tangent line. f(2)=1.
Let y=5x+c, and 1=10+c, when we plug in (2,1), c=-9 so the equation of the tangent line is y=5x-9.

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