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

Answer 1

Elijah Abram

#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.

#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 =>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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Answer 2

Scarlett Allison

To find the tangent line of f(x) = 3-2x at x=-1, we need to find the derivative of the function and evaluate it at x=-1. The derivative of f(x) is -2. Evaluating the derivative at x=-1, we get -2. Therefore, the equation of the tangent line is y = -2(x+1) + f(-1). Simplifying this equation gives us y = -2x - 1.

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Answer from HIX Tutor

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