Question

Find an equation of the line that is tangent to the graph of f and parallel to the given line.

function: f(x) = x2 − 6
line: 2x + y = 0

Answer 1

Solve for y:

2x+y=0

Add -2x to both sides

y=-2x

The slope is m=-2

Find the derivative for f(x) = x² − 6

f'(x)=2x^2-1-0=2x

Make f'(x)=m

2x=-2

Divide by 2 both sides

x=-1

Substitute in f(x)

f(-1)=(-1)²-6=1-6=-5

Use the formula

y=m(x-x₀)+f(a)

y=-2(x-(-1))+(-5)=-2(x+1)-5

Simplify

y=-2x-2-5

y=-2x-7