[tex]s(a) = 0.882 a^{0.842} [/tex]
s'(107) means the value of derivative of s(a) at a = 107. So, first step is to find the derivative of s(a).
[tex]s(a) = 0.882 a^{0.842} [/tex]
Taking derivative of both sides, we get:
[tex] \frac{d}{da}(s(a))= \frac{d}{da}( 0.882 a^{0.842})[/tex]
Taking the common out from right hand side of the equation:
[tex]s'(a)= 0.882\frac{d}{da}(a^{0.842})[/tex]
Applying the power rule of derivative:
[tex]s'(a) = 0.882 ( 0.842 a^{(0.842-1)}) \\ s'(a) = 0.742644 a^{-0.158} [/tex]
Now we can substitute 107 in place of a to get s'(107):
[tex]s'(107) = 0.742644( 107)^{-0.158} \\ s'(107)= 0.35494[/tex]
Thus the value of s'(107) rounded to 5 decimal places is 0.35494
