Find the open intervals where the function f(x)=-3x^3+9x^2+171 \ x-5is concave upward or concave...

Question:

Find the open intervals where the function {eq}f(x)=-3x^3+9x^2+171 \ x-5 {/eq} is concave upward or concave downward.

Concavity:

A function {eq}f {/eq} is concave down at the set of points in its domain at which its second derivative {eq}f'' {/eq} is negative.

{eq}f {/eq} is concave up at the set of points in its domain at which its second derivative {eq}f'' {/eq} is positive.

The given function is defined for all real numbers.

Using the second derivative to find the set of points at which the given function is concave up...

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