This problem tests calculating new functions from old ones:
From the table below calculate the quantities asked for:
\(x\)
\(-2\)
\(-5\)
\(-1\)
\(4\)
\(10\)
\(2\)
\(f(x)\)
\(19\)
\(184\)
\(4\)
\(-41\)
\(-821\)
\(-5\)
\(g(x)\)
\(-10\)
\(-130\)
\(-2\)
\(68\)
\(1010\)
\(10\)
\(f'(x)\)
\(-22\)
\(-97\)
\(-9\)
\(-34\)
\(-262\)
\(-6\)
\(g'(x)\)
\(13\)
\(76\)
\(4\)
\(49\)
\(301\)
\(13\)
\(f(-1)/( g(-1) +5)\)
\((fg)(2)\)
\((f+g)'(-1)\)
\((f/g)'(-1)\)
If \(h(x)=g(f(x))\), calculate \(h'(2)\).
You can earn partial credit on this problem.