What is the extreme y=12x^{5/7}+5x^{12/7} ?

The extreme y=12x^{5/7}+5x^{12/7} is Minimum(-1,-7)

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extreme y=12x^{5/7}+5x^{12/7}

extreme points

y = 12 x^{\frac{5}{7}} + 5 x^{\frac{12}{7}}

Minimum (- 1, - 7)

Solution steps

f^{'} (x) = \frac{60 + 60 x}{7 x ^{\frac{2}{7}}}

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 1

into

12 x^{\frac{5}{7}} + 5 x^{\frac{12}{7}} : - 7

Minimum (- 1, - 7)

y = x^{3} - 3 x^{2} + 7 x - 10

f (x) = - \frac{10}{3} x^{3} - \frac{31}{2} x^{2} - 3 x + 4

f (x) = \frac{x ^{2} + 7 x + 13}{x + 4}

\frac{( 5 x - 8 )}{x}

f (x) = sin (x), - 5 \leq x \leq 6

What is the extreme y=12x^{5/7}+5x^{12/7} ?
The extreme y=12x^{5/7}+5x^{12/7} is Minimum(-1,-7)