find and simplify the difference quotient \\( \\frac { f ( x + h ) - f ( x ) } { h } \\), \\( h \\neq 0 \\)…

find and simplify the difference quotient \\( \\frac { f ( x + h ) - f ( x ) } { h } \\), \\( h \\neq 0 \\) for the given function.\n\n\\( f ( x ) = - 9 x \\)\n\n\\( \\frac { f ( x + h ) - f ( x ) } { h } = \\square \\) (simplify your answer.)

find and simplify the difference quotient \\( \\frac { f ( x + h ) - f ( x ) } { h } \\), \\( h \\neq 0 \\) for the given function.\n\n\\( f ( x ) = - 9 x \\)\n\n\\( \\frac { f ( x + h ) - f ( x ) } { h } = \\square \\) (simplify your answer.)

Answer

Explanation:

Step1: Find ( f(x + h) )

Given ( f(x)=-9x ), substitute ( x) with ( x + h) in ( f(x)). ( f(x + h)=-9(x + h)=-9x-9h )

Step2: Substitute ( f(x + h)) and ( f(x)) into the difference quotient formula

(\frac{f(x + h)-f(x)}{h}=\frac{(-9x - 9h)-(-9x)}{h}) Simplify the numerator: ((-9x-9h + 9x)) (\frac{-9x-9h + 9x}{h}=\frac{-9h}{h})

Step3: Simplify the expression

Since (h\neq0), cancel out the common factor (h) in the numerator and denominator. (\frac{-9h}{h}=-9)

Answer:

(-9)