Bruce Partridge

2022-02-16

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

dinela24k

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
$5=\left(-2\right)\left(-1\right)+c⇒c=3.$
Hence the equation of the required tangent line to the function at the given point is
y=-2x+3.

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