OME 1964 Problem 2

The RTP tax is a function $f(x)$ , where $x$ is the total of the annual profits (in pesetas). Knowing that:

a) $f(x)$ is a continuous function b) The derivative $\frac{df(x)}{dx}$ on the interval $0 \leq 6000$ is constant and equals zero; in the interval $6000< x < P$ is constant and equals $1$ ; and when $x>P$ is constant and equal 0.14. c) $f(0)=0$ and $f(140000)=14000$ .

Determine the value of the amount $P$ (in pesetas) and represent graphically the function $y=f(x)$ .