<s>[INST] Calculus : Plug in value into a derivative? $$ f(x) = x^3-2x^2-6x $$
after derivative
$$ 3x^2-4x-6 $$
If u plugin x=1,2,3,4,5 
as a result:
$$ 3(1)^2-4(1)-6=-7 $$
$$ 3(2)^2-4(2)-6=-2 $$
$$ 3(3)^2-4(3)-6=9 $$
I know it means the slope of the current point on the curve or instantaneous rate of change 
Look at the answer 9 what is it actually mean?Is there any relationshiop between x=3 and x=4? an increment?
 [/INST] For $x=1$ :
$$f(1)=(1)^3-2(1)^2-6(1)=-7$$
$$f'(1)=3(1)^2-4(1)-6=-7$$
This means that at point $(1\:,\:-7)$ the slope of the tangent is $=-7$ .
For $x=2$ :
$$f(2)=(2)^3-2(2)^2-6(2)=-12$$
$$f'(2)=3(2)^2-4(2)-6=-2$$
This means that at point $(2\:,\:-12)$ the slope of the tangent is $=-2$ .
For $x=3$ :
$$f(3)=(3)^3-2(3)^2-6(3)=-9$$
$$f'(3)=3(3)^2-4(3)-6=9$$
This means that at point $(3\:,\:-9)$ the slope of the tangent is $=9$ .
For $x=4$ :
$$f(4)=(4)^3-2(4)^2-6(4)=8$$
$$f'(4)=3(4)^2-4(4)-6=26$$
This means that at point $(4\:,\:8)$ the slope of the tangent is $=26$ .
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