Question

How do you find an equation of the tangent line to the curve `y = x - x^5` at x=3?

Answer 1

Answer: The tangent line is: `y=-404x+972`

You can use the formula: `y-f(x_0)=f'(x_0)(x-x_0)`

First you calculate
`f'(x)=-5x^4+1`
`f'(3)=-5*3^4+1=-5*81+1=-404`

Next you calculate
`f(3)=-3^5+3=-243+3=-240`

Now you substitute `f'(3)` and `f(3)` in the formula:
`y+240=-404(x-3)`
`y+240=-404x+1212`
`y=-404x+972`