Question

what's the derivative of f(x)=4?

Answer 1

0

Answer 2

how did you get that?

Answer 3

Think of the equations as:
\[f(x)=4x^0\]
because any number (or variable in this case) to the zero power is the same as 1.
Using the power rule ...\[f \prime(x)=0*4.... = 0\]
notice that I'm ignoring the rest of the variable terms as multiplying by the 0 power zeros the entire answer. So the deriviative is 0.
Think of it this way... The derivative is the slope of a line tangent to our graph at some point. BUT, y=4 is a flat line. So ANY tangent along this horizontal line will have a slope of zero.