Bruce Partridge

2022-02-16

How do you find the tangent line of f(x)=3-2x at x=-1?

dinela24k

Beginner2022-02-17Added 7 answers

Explanation:

At x=-1, f(-1)=3-2(-1)=5

So the tangent touches the function at the point (-1,5).

The gradient of the tangent is the derivative of the function.

$\therefore$ f'(x)=-2 and in particular f'(-1)=-2.

The tangent is a straight line so has equation y=mx+c.

We may substitute the point (-1,5) in to obtain

$5=(-2)(-1)+c\Rightarrow c=3.$

Hence the equation of the required tangent line to the function at the given point is

y=-2x+3.

At x=-1, f(-1)=3-2(-1)=5

So the tangent touches the function at the point (-1,5).

The gradient of the tangent is the derivative of the function.

The tangent is a straight line so has equation y=mx+c.

We may substitute the point (-1,5) in to obtain

Hence the equation of the required tangent line to the function at the given point is

y=-2x+3.