What is the equation of the line normal to f(x)=(x-1)(x+2) at x=0?

1 Answer
Jan 14, 2018

y=x-2

Explanation:

f(x) = (x-1)(x+2)

Firstly, just expand the brackets so:

f(x) = x^2+x-2

Differentiate:

f'(x)= 2x+1

Find f'(0)

f'(0) = 2(0)+1=1

So we now the gradient of the line is is 1.

We need a point on the line and we know it should pass through the point: (0,f(0)). So find this point:

f(0) = (0)^2+(0)-2=-2

So m=1 and (a,b)=(0,-2).

Substitute into the equation of a line:

y-b=m(x-a)

y-(-2)=(1)(x-0)

->y=x-2

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