What is the slope of the line normal to the tangent line of $f(x) = 2x-2$ at $x= 3$ ?

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Answer 1 · 2018-05-08T10:56:56

$"Slope"=2$

A graph of $y=f(x)=mx+c$ will always have a gradient of $m$ .

So, when we have $f(x)=2x-2$ , the gradient is always $2$

This can be shown by differentiation:

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

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

What is the slope of the line normal to the tangent line of f(x) = 2x-2 f(x) = 2x-2 at x= 3 x= 3 ?