For f(x)=x^{5}-x^{3}+x what is the equation of the tangent line

Cian Orr

Cian Orr

Answered question


For f(x)=x5x3+x what is the equation of the tangent line at x=3?

Answer & Explanation



Beginner2022-02-16Added 6 answers

The gradient of the tangent line to the curve of f at the point 3 will be equal to the derivative of the function at the point 3.
But at 3, the function itself has value
Therefore the point with co-ordinates (x,y)=(3,219) is the point of contact of the tangent with the curve and hence lies on the tangent line so satisfies its equation, so we can substitute it in to yield
from which we obtain c=918.
Thus the equation of the required tangent line is y=379x918.

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