Step 1a

To find the derivative of the function \$"f"("x") = 4"x"^2 + 7"x" - 11\$, we can use the power rule and the sum rule of differentiation.

The power rule states that the derivative of a term of the form \$"ax"^"n"\$ is given by \$"d"/"dx"("ax"^"n") = "anx"^("n" - 1)\$.

Explanation: Apply the power and sum rules to solve the given derivative function.

Step 1b

Apply the power rule to each term of f(x), and then simplify:

\$ "d"/"dx" "f"("x") = "d"/"dx"(4"x"^2) + "d"/"dx"(7"x") + "d"/"dx"(-11) \$

\$ "f"'("x") = 2 * 4"x"^(2 - 1) + 1 * 7"x"^(1 - 1) + 0 \$

\$ "f"'("x") = 8"x" + 7 \$

Therefore, the derivative of the function
\$f("x") = 4"x"^2 + 7"x" - 11\$ is \$"f"'("x") = 8"x" + 7\$.

Explanation: Apply derivative rules to the function, then simplify to find the derivative of the function \$"f"'("x") = 8"x" + 7\$.