Question

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

Answer 1

The equation is `y=-5(x-2)=-5x+10`

Explanation:

The derivative is `f'(x)=-2x-1`, so that the slope of the tangent line at `x=2` is `f'(2)=-4-1=-5`.

Since `f(2)=-4-2+6=0`, it follows that the equation is `y=-5(x-2)=-5x+10`.