For the function f, construct and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h }$
-$f ( x ) = 9 | x | + 4 x$
A) -3h
B) $\frac { 9 | x + h | - 4 h - 9 | x | } { h }$
C) -5h
D) $\frac { - 9 | x + h | - 5 h + 9 | x | } { h }$

Question

For the function f, construct and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h }$
-$f ( x ) = 9 | x | + 4 x$
A)  -3h
B) $\frac { 9 | x + h | - 4 h - 9 | x | } { h }$
C)  -5h
D) $\frac { - 9 | x + h | - 5 h + 9 | x | } { h }$

Quizplus · Accepted Answer

The difference quotient for the function $f(x) = 9|x| + 4x$ is calculated by substituting $f(x+h)$ and $f(x)$ into the formula $\frac{f(x+h) - f(x)}{h}$. This results in $\frac{9|x+h| + 4(x+h) - (9|x| + 4x)}{h}$, which simplifies to $\frac{9|x+h| - 9|x| + 4h}{h}$, matching choice B.

For the Function F, Construct and Simplify the Difference Quotient f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​

For the Function F, Construct and Simplify the Difference Quotient $\frac { f ( x + h ) - f ( x ) } { h }$