$\backslash$table$[[x,-3,0,3,6],[f(x),-5,4,1,7],[f^{\text{'}}(x),-1,2,-2,4]]$

The table above gives values of a twice$-$differentiable function $f$ and its first derivative $f^{\text{'}}$ for selected values of $x.$ Let $g$ be the function defined by $g(x)=f(x^2-x).$

$($a$)$ What is the value of $g^{\text{'}}(3)?$

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On your AP Exam, you will handwrite your responses to free$-$response questions in a test

$($b$)$ It is known that $g^{\text{'}\text{'}}(0)=-1.$ What is the value of $f^{\text{'}\text{'}}(0)?($c$)$ Is there a value $c,$ for $g(c)=5h{h}^{\text{'}}(x)=4e^{cosx}x-3x0hf-3x00,$ such that $g(c)=5?$ Justify your answer.

$(d)$ Let $hbe$ the function with derivative given $by{h}^{\text{'}}(x)=4e^{cosx}.At$ what value $ofxin$ the interval $-3x0$ does the instantaneous rate $of$ change $ofh$ equal the average rate $of$ change $off$ over the interval $-3x0?$