Weird result to a simple derivative question

[Femme_physics]

I am told to write the value of a the derivative at a certain point next to each function. And to find the point/s

f(x) = x²

f ' (x) = -6

so I figured I just do

f ' (x) = 2x

f ' (-6) = 2 x (-6) = -12

But they tell me the answer is

(-3, 9)

 

[Char. Limit]

The problem is that f'(x)=-6, and what you plugged in is equivalent to x=-6.

You got the derivative right, but you need to set f'(x) to -6, not x.

 

[Femme_physics]

Oh... I see! thanks :)

 

[Ouabache]

Another way to look at it...
You were given value of the derivative
$f'(x) = -6$ (eq 1)
and you found the derivative of equation $f(x)=x^2$ to be
$f'(x) = 2x$ (eq 2)

The left side of equations 1 & 2 are equal,
therefore the right sides are also,
so -6 = 2x and you can solve for x.

To find y, substitute this x into the original equation of f(x)
and you will obtain the same point you noted from the solution guide.