Answer:
(-1, -4)
Step-by-step explanation:
The critical point is the point where the slope is 0 or undefined.
This is a parabola (quadratic), so there wont be any undefined points, only a critical point where slope is 0.
We need to take the derivative of the function and set it equal to 0 to find the x coordinate of the critical point. Then we plug in that x point into original equation to find the y coordinate.
Lets see the power rule of differentiation before we differentiate this function.
Power Rule: [tex]\frac{d}{dx}(x^n)=nx^{n-1}[/tex]
Also, differentiation a constant is always 0!!
Now, differentiating:
[tex]f(x)=x^2+2x-3\\\frac{d}{dx}(f(x))=2x+2[/tex]
Now, we set equal to 0 and find x:
[tex]2x+2=0\\2x=-2\\x=\frac{-2}{2}\\x=-1[/tex]
Now, we find y:
[tex]f(x=-1)=(-1)^2+2(-1)-3=-4[/tex]
So,
x = -1
y = -4
The critical point is (-1, -4)
