$\text { Use the formula } f ^ { \prime } ( x ) = \lim _ { z \rightarrow x } \frac { f ( z ) - f ( x ) } { z - x } \text { to find the derivative of the function. }$
-$f ( x ) = 4 x ^ { 2 } + 3 x + 5$
A) $4 x + 3$
B) $8 x ^ { 2 } + 3 x$
C) $8 x + 3$
D) $8 x$

Question

Quizplus · Accepted Answer

To find the derivative $f'(x)$ of the function $f(x) = 4x^2 + 3x + 5$, we apply the power rule for differentiation directly (the given formula is the definition of the derivative, but for polynomial functions like this, direct application of differentiation rules is more straightforward). The derivative of $4x^2$ is $8x$, the derivative of $3x$ is $3$, and the derivative of a constant $5$ is $0$. Therefore, $f'(x) = 8x + 3$.

- f(x)=4x2+3x+5f ( x ) = 4 x ^ { 2 } + 3 x + 5f(x)=4x2+3x+5

- $f ( x ) = 4 x ^ { 2 } + 3 x + 5$