Find

f$($a$).$

f$($x$)=3$x$25$x $+1$

Step $1$

Recall that the derivative of a function f at a number a$,$ denoted by

f$($a$),$

is given by the following, if this limit exists.

f$($a$)=$lim$$h$0$

f$($a $+$ h$)$ f$($a$)$h

$$

We are given

f$($x$)=3$x$25$x $+1.$

We apply this definition using the given function as follows.

f$($a$)=$lim$$h$0$

f$($a $+$ h$)$ f$($a$)$h

$=$lim$$h$0$

$3($a $+$ h$)25$

$+1$

$(3$a$25$a $+1)$h