Find the equations of the tangent and normal to the given curves at the indicatedpoints:(i) `y=x^4-6x^3+13 x^2-10 x+5`at `(0, 5)`(ii) `y=x^4-6x^3+13 x^2-10 x+5`at `(1, 3)`(iii) `y=x^3`at `(1, 1)`(iv) `y=x^2`at `(0, 0)`(v) `x = cos t ,y=sin t at t=pi/4`

Explanation

To find the equations of the tangent and normal to the given curves at the indicated points, we will follow these steps for each point:

1. **Differentiate the function to find the slope of the tangent.**
2. **Evaluate the derivative at the given point to find the slope of the tangent.**
3. **Use the point-slope form of the equation of a line to find the equation of the tangent.**
4. **Find the slope of the normal (which is the negative reciprocal of the slope of the tangent).**
5. **Use the point-slope form again to find the equation of the normal.**

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