Question

Find the critical point of the function f(x) = x2 + 2x - 3.

Answer 1

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:  $\frac{d}{dx}(x^n)=nx^{n-1}$

Also, differentiation a constant is always 0!!

Now, differentiating:

$f(x)=x^2+2x-3\\\frac{d}{dx}(f(x))=2x+2$

Now, we set equal to 0 and find x:

$2x+2=0\\2x=-2\\x=\frac{-2}{2}\\x=-1$

Now, we find y:

$f(x=-1)=(-1)^2+2(-1)-3=-4$

So,

x = -1

y = -4

The critical point is  (-1, -4)