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Sagot :
Given function in the question is,
[tex]f(x)=2-5x-x^2[/tex]
To find the difference coefficient for the given function, we use the expression as [tex]\frac{f(3+h)-f(3)}{h}[/tex].
[tex]f(3+h)=2-5(3+h)-(3+h)^2[/tex]
[tex]=2-15-5h-(9+h^2+6h)[/tex]
[tex]=(2-15-9)-(5h+6h)-h^2[/tex]
[tex]=-22-11h-h^2[/tex]
[tex]=-(22+11h+h^2)[/tex]
[tex]f(3)=2-5(3)-(3^2)[/tex]
[tex]=2-15-9[/tex]
[tex]=-22[/tex]
Now substitute these values in the expression for the difference coefficient,
[tex]\frac{f(3+h)-f(3)}{h}=\frac{-(22+11h+h^2)-(-22)}{h}[/tex]
[tex]=\frac{-22-11h-h^2+22}{h}[/tex]
[tex]=\frac{-11h-h^2}{h}[/tex]
[tex]=-(11+h)[/tex]
Therefore, Value of the difference quotient for the given function is[tex]-(11+h)[/tex].
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