Answer
0
Work Step by Step
The slope of the tangent line through the point on the graph of $f$ where $x=a$
is given by the instantaneous rate of change, or derivative
$m_{tan}=$ slope of tangent $=$ instantaneous rate of change$=$derivative
$=f^{\prime}(a)=\displaystyle \lim_{h\rightarrow 0}\frac{f(a+h)-f(a)}{h} ,$
assuming the limit exists.
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Let P be $(a,f(a))$, since it is on the graph of f.
From the graph, we read (estimate) two points from the tangent line at P:
(0,5) and (1,5)
(we estimate the line as being horizontal )
The slope of the tangent line = 0
(horizontal lines have slopes 0)
so, we estimate
$f^{\prime}(a)=m=0$
