## Equation of a Tangent Line: Problems and Solutions

### 2 What are your thoughts and questions?

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Anonymous

Y=x³at the point 1,1 give the solution

Matheno

Following the approach outlined in the SUMMARY box above:

1. The slope of the tangent line at (1,1) equals the derivative at that point. Since $y=f(x)= x^3,$ the derivative is $y’=f'(x) =3x^2.$ Hence the slope of the tangent line at $x_0 = 1$ is $m_{tangent} = f'(1) = 3.$

2. Then we can write the equation of this tangent line, using the point-slope form of the line that has slope $m_{tangent} = 3$ and contains the point (1,1):
$$y – 1 = 3(x-1)$$

Does that provide the solution you were after? We hope so!