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Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)f(x)=36x−2x^2

Respuesta :

MrRoyal

Answer:

[tex]x =9[/tex] --- the critical point

Step-by-step explanation:

Given

[tex]f(x) =36x -2x^2[/tex]

Required

Determine the critical numbers

First, we differentiate f(x)

[tex]f'(x) = 36 - 4x[/tex]

Set to 0 and solve for x

[tex]36 -4x = 0[/tex]

Make 4x the subject

[tex]4x = 36[/tex]

Solve for x

[tex]x =36/4[/tex]

[tex]x =9[/tex]

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