Calculus Examples
f(x)=x2f(x)=x2
Step 1
Step 1.1
Differentiate using the Power Rule which states that ddx[xn]ddx[xn] is nxn-1nxn−1 where n=2n=2.
f′(x)=2xf'(x)=2x
Step 1.2
The first derivative of f(x)f(x) with respect to xx is 2x2x.
2x2x
2x2x
Step 2
Step 2.1
Set the first derivative equal to 00.
2x=02x=0
Step 2.2
Divide each term in 2x=02x=0 by 22 and simplify.
Step 2.2.1
Divide each term in 2x=02x=0 by 22.
2x2=022x2=02
Step 2.2.2
Simplify the left side.
Step 2.2.2.1
Cancel the common factor of 22.
Step 2.2.2.1.1
Cancel the common factor.
2x2=02
Step 2.2.2.1.2
Divide x by 1.
x=02
x=02
x=02
Step 2.2.3
Simplify the right side.
Step 2.2.3.1
Divide 0 by 2.
x=0
x=0
x=0
x=0
Step 3
Step 3.1
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Step 4
Step 4.1
Evaluate at x=0.
Step 4.1.1
Substitute 0 for x.
(0)2
Step 4.1.2
Raising 0 to any positive power yields 0.
0
0
Step 4.2
List all of the points.
(0,0)
(0,0)
Step 5