Question

Given ( f(x) = 3x² ), find ( f'(x) ). Then state whether ( f'(x) ) is a function.

a. ( Y = 6x ), ( f'(x) ) is not a function.
b. ( Y = 6x² ), ( f'(x) ) is a function.
c. ( Y = 2x³ ), ( f'(x) ) is not a function.
d. ( Y = x² + 2 ), ( f'(x) ) is a function.

Answer 1

To find f'(x), differentiate the function f(x) = 3x² with respect to x. The derivative is f'(x) = 6x. Option b (Y = 6x²), (f'(x)) is a function.

Step-by-step explanation:

To find f'(x), we need to differentiate the function f(x) = 3x² with respect to x. Differentiating a power function involves bringing down the exponent and reducing the exponent by 1. So, f'(x) = 6x. This means that the derivative of the function f(x) = 3x² is f'(x) = 6x.

Now, to determine if f'(x) is a function, we need to check if it passes the vertical line test. The derivative of any polynomial function is always a function because it is a linear function in this case. So, the correct answer is option b. (Y = 6x²), (f'(x)) is a function.