Question

Use f prime left parenthesis x right parenthesis equals ModifyingBelow lim With h right arrow 0 StartFraction f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis Over h EndFractionf′(x)=limh→0 f(x+h)−f(x) h to find the derivative at x for the given function. s left parenthesis x right parenthesis equals 2 x plus 6s(x)=2x+6 s prime left parenthesis x right parenthesiss′(x)equals=nothing

Answer 1

$$ Solution:$

$s(x) = 2x+6$

$$ The derivative of function $ f(x) $ is given by:$

$f'(x) = \lim_{h \rightarrow 0} \frac{f(x+h) - f(x)}{h}$

$i.e., \ \ \ s'(x) = \lim_{h \rightarrow 0} \frac{s(x+h) - s(x)}{h}$

$i.e., \ \ \ s'(x) = \lim_{h \rightarrow 0} \frac{2(x+h) +6 - 2x -6}{h}$

   $= \lim_{h \rightarrow 0} \frac{2x+2h +6 - 2x -6}{h}$

   $= \lim_{h \rightarrow 0} \frac{2h }{h}$

   $= \lim_{h \rightarrow 0} (2)$

   $= 2$

$$ Therefore, the derivative of $ s(x) $ is: \ $ s'(x) = 2$