Consider the function \( f(x) = 12x^5 + 45x^4 - 360x^3 + 7 \).

\( f(x) \) has inflection points at \( x \) values (reading from left to right) \( x = D \), \( x = E \), and \( x = F \) where \( D \) is , \( E \) is , and \( F \) is __.

Question

01-08-2024
Mathematics

High School

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Consider the function \( f(x) = 12x^5 + 45x^4 - 360x^3 + 7 \).

\( f(x) \) has inflection points at \( x \) values (reading from left to right) \( x = D \), \( x = E \), and \( x = F \) where \( D \) is , \( E \) is , and \( F \) is __.

Answer :

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CarrLola CarrLola · Answer 1 · 2025-03-19T16:31:12-04:00

The inflection points D, E, and F of the function f(x)=12x^5+45x^4-360x^3+7, we must calculate the second derivative, set it to zero, and solve for x.

The inflection points of a polynomial function, which is a concept in calculus related to finding where the concavity of a graph changes. Inflection points occur where the second derivative of the function is equal to zero and changes sign.

To determine the inflection points for the function f(x)=12x5+45x4-360x3+7, we need to find the second derivative, set it to zero, and solve for x.

First, we find the first derivative f'(x):

f'(x) = 60x4+180x3-1080x2

Then, we find the second derivative f''(x):

f''(x) = 240x3+540x2-2160x

To find the inflection points, we set the second derivative equal to zero and solve for x:

240x3+540x2-2160x = 0

Solve for x to find the values D, E, and F where the inflection points occur.

Consider the function \( f(x) = 12x^5 + 45x^4 - 360x^3 + 7 \).\( f(x) \) has inflection points at \( x \) values (reading from left to right) \( x = D \), \( x = E \), and \( x = F \) where \( D \) is __________, \( E \) is __________, and \( F \) is __________.

Answer :

Other Questions

Consider the function \( f(x) = 12x^5 + 45x^4 - 360x^3 + 7 \).

\( f(x) \) has inflection points at \( x \) values (reading from left to right) \( x = D \), \( x = E \), and \( x = F \) where \( D \) is , \( E \) is , and \( F \) is __.