Question

at which point will the curve have a slope?

Answer 1

Find \(f'(x)\), then solve for \(f'(x)=0\), \(f'(x)=3\), and \(f'(x)=-3\).

In each equation, you'll have to solve for \(x\).

Answer 2

so if i plug in 0, 3 and -3 to find the y's would it be wrong?

Answer 3

@SithsAndGiggles

Answer 4

i plugged in and i got:

x=0 y=-3
x=3 y=-16
x=-3 y=18

Answer 5

@SithsAndGiggles

Answer 6

If \(f(x)=x^2-4x-3\), then \(f'(x)=2x-4\).

Now solve each equation for \(x\):
\[\begin{cases}
2x-4=0\\
2x-4=3\\
2x-4=-3
\end{cases}\]
Left side of each equation is the derivative (slope) of the function for some x. Your goal here is to find for which values of x does the function f have the slope ... (right side of each equation). Does that make sense?

In other words, you're given the slope, and you must find when the function has that slope.