given the following function, determine the difference quotient, \\( \\frac { f ( x + h ) - f ( x ) } { h }…
given the following function, determine the difference quotient, \\( \\frac { f ( x + h ) - f ( x ) } { h } \\).\n\\( f ( x ) = 4 x - 1 \\)
Answer
Explanation:
Step1: Find (f(x + h))
Substitute (x+h) into (f(x)): (f(x + h)=4(x + h)-1=4x+4h - 1)
Step2: Calculate (f(x + h)-f(x))
(f(x + h)-f(x)=(4x + 4h-1)-(4x - 1)) (=4x+4h - 1-4x + 1) (=4h)
Step3: Compute (\frac{f(x + h)-f(x)}{h})
(\frac{f(x + h)-f(x)}{h}=\frac{4h}{h})
Answer:
(4)