Light sources are placed at two fixed points Q and R which are 1 metre apart. The source at R is twice as intense as that at Q. The total illumination at a point P on the line QR x metres distant from Q is cf(x) where c is a positive constant and

Evaluate f(0.3),  f(0.4) and f(0.5) and find the quadratic function

which passes through (0.3, f(0.3)), (0.4, f(0.4)) and (0.5, f(0.5)). Use this function to estimate the value of x at which the minimum of f(x) occurs. Compare your result with that obtained by calculus methods.

1 f(x)= + 2 (1-x) 0