Derivative Concepts: What is a derivative function?

$\backslash$table$[[\backslash$table$[[$a$.$ It is the inverse$],[$of the original$],[$function$.]],\backslash$table$[[$b$.$ It is the original$],[$function with only a$],[$positive domain.$]],\backslash$table$[[$cr instantaneous rate$],[$or instange, at every$],[$of change,$],[$point of the function.$]],$d$.$ None of these,$]]$

Which is the correct vertex of the function $f(x)=-2x^2-4x+1$ and is it a maximum or a minimum for the function??

a$.$ minimum at $(-1,3)$

b$.$ minimum at $(3,-1)$

c$.$ maximum at $(-1,3)$

d$.$ maximum at $(3,-1)$

For the function $h(x)=-2x^2+6x+,$ find $h^{\text{'}}(x).$

a$.h^{\text{'}}(x)=-2x^2+6$

b$.h^{\text{'}}(x)=-4x+6+$

c$.h^{\text{'}}(x)=-4x$

d$.h^{\text{'}}(x)=-4x+6$

Derivative Concept: In which graph is the derivative always positive?

For the function $h(x)=-2x^2+6x+,$ find $h^{\text{'}}(x).$

a$.h^{\text{'}}(x)=-2x^2+6$

b$.h^{\text{'}}(x)=-4x+6+$

c$.h^{\text{'}}(x)=-4x$

d$.h^{\text{'}}(x)=-4x+6$

Derivative Concept: In which graph is the derivative always positive?