Answer :
Final answer:
To uncover inflection points D, E and F in the polynomial function f(x) = 12x^5 +60x^4 - 100x^3+5, you should first find the function's derivative and then its second derivative. The inflection points are where the second derivative changes sign.
Explanation:
The function in question, f(x) = 12x^5 +60x^4 - 100x^3+5 is a fifth-degree polynomial. To find the inflection points of a function, one must determine where the second derivative changes sign.
The first step involves finding the derivative of the function, followed by taking the second derivative. Critical points will occur at the points where the second derivative equals zero, and the inflection point is where the second derivative changes sign.
Before determining these points, we have the function's second derivative. The second derivative of the function can be calculated by taking the derivative of the first derivative. Finally, we can track where this derivative changes sign to find the function's inflection points (D, E, F).
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