What is the extreme y= 1/2 x^2+((14-3x)/4)^2 ?

The extreme y= 1/2 x^2+((14-3x)/4)^2 is Minimum(42/17 , 98/17)

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extreme y= 1/2 x^2+((14-3x)/4)^2

extreme points

y = \frac{1}{2} x^{2} + (\frac{14 - 3 x}{4})^{2}

Minimum (\frac{42}{17}, \frac{98}{17})

Solution steps

f^{'} (x) = \frac{17 x - 42}{8}

Find intervals:

Decreasing

: - \infty < x < \frac{42}{17},

Increasing

: \frac{42}{17} < x < \infty

Plug

x = \frac{42}{17}

into

\frac{1}{2} x^{2} + (\frac{14 - 3 x}{4})^{2} : \frac{98}{17}

Minimum (\frac{42}{17}, \frac{98}{17})

93000 x - 36000

f (x) = x^{4} - 32 x^{2} - 10

f (x, y) = x - 5 y

f (x) = x^{4} (x - 5) + 4

f (x) = x^{2} - \frac{54}{x}

What is the extreme y= 1/2 x^2+((14-3x)/4)^2 ?
The extreme y= 1/2 x^2+((14-3x)/4)^2 is Minimum(42/17 , 98/17)