Questions: f(x)=-4x^3-84x^2+6x-2 Step 2 of 2: Locate any points of inflection. Enter your answer as (x, y)-pairs.

Transcript text: \[ f(x)=-4 x^{3}-84 x^{2}+6 x-2 \] Step 2 of 2: Locate any points of inflection. Enter your answer as ( $x, y$ )-pairs.

Solution

Step 1: Find the second derivative $f''(x)$

The second derivative of the function is: $f''(x) = - 24 \left(x + 7\right)$

Step 2: Solve $f''(x) = 0$

The potential points of inflection are found by solving $f''(x) = 0$, which gives: $x = \left\{-7\right\}$

Step 3: Determine the sign change of $f''(x)$

After testing values around the potential points, the confirmed points of inflection are at $x = -7$

Step 4: Calculate the corresponding $y$ values

For $x = -7$, $y = -2788$

Point of inflection at ($x$, $y$) = ($-7, -2788$)

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