# f(x)=4x^3+6x^2-24x+6 a. Find the interval on which f is increasing and decreasing. b. Find the local maximum and local minimum value of f c. Find the inflection point d.Find the interval on which f is concave up and down

Luca B. | Certified Educator

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a) You need to perform the first derivative test , hence you should find first derivative such that:

`f'(x) = 12x^2 + 12x - 24`

You need to solve the equation f'(x) = 0 such that:

`f'(x) = 0 =gt 12x^2 + 12x - 24 = 0`

`x^2 + x - 2 = 0`

`x^2 + x - 1 - 1 = 0 =gt (x^2-1) + (x-1) = 0`

(x-1)(x+1+1) = 0 => x - 1 = 0 => x = 1

`x + 2 = 0 =gt x = -2`

You need to use the signs rule for a quadratic function, hence, between the roots, the values...

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