Perform a first derivative test on the function \( f(x)=2 x^{3}+6 x^{2}-48 x+6 ;[-4,6] \) a. Locate the critical points of the given function. b. Use the First Derivative Test to locate the local maximum and minimum values. c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist).

\( f ^ { \prime \prime } ( x ) = 12 x ^ { \wedge } 2 - 48 x + 32 \)

Что такое производная функции? a. 1 b. Предел значения этой функции c. \( \lim _{x \rightarrow 0} \frac{\Delta y}{\Delta x} \) d. 0 е.

a. \( \lim _{x \rightarrow 1} \frac{3-\sqrt{10-x}}{x-1} \)

10. (3 points) Find the derivative of \( y=x^{2 x} \) \( \begin{array}{ll}\text { (A) } y^{\prime}=(2 \ln (x)+2) & \text { (B) } y^{\prime}=x^{2 x} \cdot(2 \ln (x)+1) \\ \text { C } y^{\prime}=2 x \cdot x^{2 x-1} & \text { (D) } y^{\prime}=x^{2 x} \cdot(2 \ln (x)+2)\end{array} \)

\( \int \frac { x ^ { 2 } - 2 x - 1 } { ( x - 1 ) ^ { 2 } ( x ^ { 2 } + 1 ) } d x \)