Evaluate the function at the indicated value.
-Find $\frac { f ( x + h ) - f ( x ) } { h }$ when $f ( x ) = x ^ { 2 } + 7 x + 4$
A) 1
B) $2 x + h + 4$
C) $2 x + h + 7$
D) $\frac { 2 x ^ { 2 } + 2 x + 2 x h + h ^ { 2 } + h + 8 } { h }$

Question

Quizplus · Accepted Answer

To find $\frac { f ( x + h ) - f ( x ) } { h }$, first substitute $x + h$ into the function: $f(x + h) = (x + h)^2 + 7(x + h) + 4$. Expanding this gives $x^2 + 2xh + h^2 + 7x + 7h + 4$. Subtracting $f(x) = x^2 + 7x + 4$ from this yields $2xh + h^2 + 7h$. Dividing by $h$ simplifies to $2x + h + 7$.

Evaluate the Function at the Indicated Value f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​

Evaluate the Function at the Indicated Value $\frac { f ( x + h ) - f ( x ) } { h }$