# Equation of a straight line which is tangent to a curve

For the curve f(x) = x - 1/3x^2 (one third x squared), find the equation of the straight line which is tangent to this curve at the point x = 1.

See attachment for diagram.

https://brainmass.com/math/derivatives/equation-straight-line-which-tangent-curve-5295

#### Solution Preview

For the curve f(x) = x - 1/3x^2 (one third x squared), find the equation of the straight line which is tangent to this curve at the point x = 1.

Equation of the curve= f(x) = x - 1/3x^2

y= x- 1/3 x ^2

Finding derivative is easy

Derivative of x ^n is n x ^ (n-1)

Thus derivative of x ^2 is

2 x ^(2-1)= 2 x ^ 1 that is 2x

Derivative of x is

x= x ^1

therefore ...

#### Solution Summary

Finds the equation of the straight line which is tangent to the curve f(x) = x - 1/3x^2.

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