Light sources are placed at two fixed points Q and R which are 1 metre apart. The

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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

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

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

g(x) = A(x 0.4) + B(x - 0.4) + C -

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.

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