# The function f(x)= (-6x^3)+(7.11x^2)+327.6936x-0.1499999999999999a) is increasing on the interval ? b) is decreasing on the interval ( , ? ) and the interval ( ?, ). c) The function has a local...

The function

f(x)= (-6x^3)+(7.11x^2)+327.6936x-0.1499999999999999

a) is increasing on the interval ?

b) is decreasing on the interval ( , ? ) and the interval ( ?, ).

c) The function has a local maximum at ?.

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The function is

f(x)= (-6x^3)+(7.11x^2)+327.6936x-0.1499999999999999

a) a function is increasing when the derivative of the function is larger than 0.

f'(x) = -18x^2 + 14.22x + 327.6936 > 0

solve this in a calculator and you will get

-3.89 < x < 4.68

b) a function is decreasing when the derivative of the function is smaller than 0.

f'(x) = -18x^2 + 14.22x + 327.6936 < 0

solve this in a calculator and you will get

x < -3.89 or x > 4.68

c) the local maximum occurs when the derivative of a function equals zero and the second derivative is smaller than 0.

f'(x) = -18x^2 + 14.22x + 327.6936 = 0

x = -3.89 or x = 4.68

f''(x) = -36x + 14.22 < 0

x > 0.395

the number that satisfies both conditions is 4.68

So the function has a local maximum at x = 4.68