Question

What is the equation of the tangent line of `f(x)=(9 + x)^2` at `x=6`?

Answer 1

`y=30x-45`

Explanation:

`f(x)=(9+x)^2`
`f'(x)=2(9+x)*1`
`f'(x)=18+2x`

since `f'(x`) is a gradient of tangent, therefore
when `x=6` it gradient, `m=18+2(6)=30`

When `x=x_1=6, f(6)=y_1=(9+6)^2=225`
Therefore,
`y-y_1=m(x-x_1)`
`y-225=30(x-6)`
`y=30x-180+225`
`y=30x-45`