f(x)=x^3
f'(x)=3x^2
Function f(x) is defined as:
f(x) = x^3
Here, we raise x to the third power, which means we multiply x by itself three times.
For example, if x = 2, then:
f(2) = 2^3
f(2) = 2 x 2 x 2
f(2) = 8
Therefore, the value of the function f(x) at x = 2 is 8.
Similarly, we can find the value of the function f(x) for other values of x. For instance, if x = -1:
f(-1) = (-1)^3
f(-1) = -1 x -1 x -1
f(-1) = -1
So, the value of the function f(x) at x = -1 is -1.
We can also graph the function f(x) on a coordinate plane. As the exponent increases from 1 to 3, the curve becomes steeper and more symmetrical, creating a characteristic shape called a cubic function.
In summary, the function f(x) = x^3 raises x to the power of 3 and provides a way to calculate the output value of the function for any input value of x.
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