What is the extreme y=2x^3-15x^2+24x-5 ?

The extreme y=2x^3-15x^2+24x-5 is Maximum(1,6),Minimum(4,-21)

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extreme y=2x^3-15x^2+24x-5

extreme points

y = 2 x^{3} - 15 x^{2} + 24 x - 5

Maximum (1, 6), Minimum (4, - 21)

Solution steps

f^{'} (x) = 6 x^{2} - 30 x + 24

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 1

into

2 x^{3} - 15 x^{2} + 24 x - 5 : 6

Maximum (1, 6)

Plug

x = 4

into

2 x^{3} - 15 x^{2} + 24 x - 5 : - 21

Minimum (4, - 21)

Maximum (1, 6), Minimum (4, - 21)

f (x) = - 7 x^{2} + 42 x + 5

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

f (x, y) = 42 x^{4} + 42 y^{4} - 4 x y + 19

y = x^{2} - 5 x - 2

f (x) = x^{3} - \frac{3 x ^{2}}{2}

What is the extreme y=2x^3-15x^2+24x-5 ?
The extreme y=2x^3-15x^2+24x-5 is Maximum(1,6),Minimum(4,-21)