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If f(x)=3x5−10x3+5, on what intervals is f″(x)>0?

Enter the (disjoint) interval(s) below using 'U' for union, '"nf" for [infinity], and "-inf" for −[infinity] if necessary.

Respuesta :

Answer:

[tex](0.7937,\infty)[/tex]

Step-by-step explanation:

we are given an algebraic function in x, such that

[tex]f(x) = 3x^5-10x^3+5[/tex]

To find when second derivative >0

For this let us find first and second derivative by successive differentiation.

[tex]f(x) = 3x^5-10x^3+5\\f'(x) =15x^4-30x^2\\f'(x)=60x^3-30[/tex]

when ii derivative >0 we have

60x^3-30>0

[tex]x^3>0.5\\x>0.7937[/tex]

f"(x)>0 in

[tex](0.7937,\infty)[/tex]

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