Question

What is the equation of the line tangent to `f(x)=x^2+5x` at `x=-1`?

Answer 1

`y=3x-1`

Explanation:

Slope of the tangent line when x = -1: `f'(x)=2x+5->f'(-1)=2(-1)+5=-2+5=3`

Point: `f(-1)=(-1)^2+5(-1)=1-5=-4, (-1,-4)`

Equation of tangent line: `y=f(-1)+f'(-1)(x--1)`

`y=-4+3(x+1)`

`y=-4+3x+3`

`y=3x-1`