The calculation of duty cycle of wide input voltage

I am trying to design a boost converter to drive an LED by using LM3478. The input voltage is not a certain value but a voltage range(6V~ 17V). The ouput voltage is about 40V. During power inductor selection ,the datasheet of LM3478 says the average inductor current should be larger than the inductor current ripple. so we can esaily get a expression :

L>D(1-D)*Vin/(2*Iout*fs),

So the duty cylce(D) should be known first.

Of course, If i want to calculate the duty cycle, a formula[Vout=Vin/(1-D) ] will be used. and here is my puzzle:

1. when i calculate the duty cycle, what value should i use for Vin, 6V or 17V ,or some value else ?

2.when i use the epression of "L>D(1-D)*Vin/(2*Iout*fs)" to calculate the inductor value, should use the value of Vin the same as above ???

The key requirement is to maintain a continuous conduction mode in the inductor.

Calculate L for the lowest and highest input voltage range, and choose the inductor value which is the largest.

The sensitivity of any formula to a parameter is it's partial derivative.

- therefore use mean & % tolerances for linear analysis

So Vin = 6~17=11.5 +/- 5.5=11.5 +/- ~50% for sensitivity summations

Or use both worst case values ...