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Popular >

extreme f(x)=-x^3+8x^2-15x

Solution

extreme points

f (x) = - x^{3} + 8 x^{2} - 15 x

Solution

Minimum (\frac{8 - 19}{3}, - 5 (8 - 19) + \frac{1024 - 173 19}{27}), Maximum (\frac{8 + 19}{3}, - 5 (8 + 19) + \frac{1024 + 173 19}{27})

Solution steps

f^{'} (x) = - 3 x^{2} + 16 x - 15

Find intervals:

Decreasing

: - \infty < x < \frac{- 19 + 8}{3},

Increasing

: \frac{- 19 + 8}{3} < x < \frac{19 + 8}{3},

Decreasing

: \frac{19 + 8}{3} < x < \infty

Plug

x = \frac{8 - 19}{3}

into

- x^{3} + 8 x^{2} - 15 x : - 5 (8 - 19) + \frac{1024 - 173 19}{27}

Minimum (\frac{8 - 19}{3}, - 5 (8 - 19) + \frac{1024 - 173 19}{27})

Plug

x = \frac{8 + 19}{3}

into

- x^{3} + 8 x^{2} - 15 x : - 5 (8 + 19) + \frac{1024 + 173 19}{27}

Maximum (\frac{8 + 19}{3}, - 5 (8 + 19) + \frac{1024 + 173 19}{27})

Minimum (\frac{8 - 19}{3}, - 5 (8 - 19) + \frac{1024 - 173 19}{27}), Maximum (\frac{8 + 19}{3}, - 5 (8 + 19) + \frac{1024 + 173 19}{27})

Popular Examples

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

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

extreme f(x)=-7x^2+42x+5 extreme points

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

extreme f(x)=2x^2+2xy+y^2+2x-3 extreme points

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

extreme f(x,y)=42x^4+42y^4-4xy+19 extreme points

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

extreme y=x^2-5x-2 extreme points

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

Frequently Asked Questions (FAQ)

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