What is the extreme 42x^3+33x^2-36x+12 ?

The extreme 42x^3+33x^2-36x+12 is Maximum(-6/7 , 1992/49),Minimum(1/3 , 47/9)

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extreme 42x^3+33x^2-36x+12

extreme points

42 x^{3} + 33 x^{2} - 36 x + 12

Maximum (- \frac{6}{7}, \frac{1992}{49}), Minimum (\frac{1}{3}, \frac{47}{9})

Solution steps

f^{'} (x) = 126 x^{2} + 66 x - 36

Find intervals:

Increasing

: - \infty < x < - \frac{6}{7},

Decreasing

: - \frac{6}{7} < x < \frac{1}{3},

Increasing

: \frac{1}{3} < x < \infty

Plug

x = - \frac{6}{7}

into

42 x^{3} + 33 x^{2} - 36 x + 12 : \frac{1992}{49}

Maximum (- \frac{6}{7}, \frac{1992}{49})

Plug

x = \frac{1}{3}

into

42 x^{3} + 33 x^{2} - 36 x + 12 : \frac{47}{9}

Minimum (\frac{1}{3}, \frac{47}{9})

Maximum (- \frac{6}{7}, \frac{1992}{49}), Minimum (\frac{1}{3}, \frac{47}{9})

f (x) = \frac{1}{9} [\frac{t ^{3}}{3} + \frac{3 t ^{2}}{2} - 28 t]

f (x, y) = 3 x + 4 x^{2} y^{3} - 5 y^{2}

f (x) = x^{2} - x y + y^{2}

5 x - 3

f (x) = - x^{3} + 3 x^{2} + 2 x

What is the extreme 42x^3+33x^2-36x+12 ?
The extreme 42x^3+33x^2-36x+12 is Maximum(-6/7 , 1992/49),Minimum(1/3 , 47/9)