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Maximum value of f(x) for x > 0 is 90 and the maximum value of g(x) for x > 0 is 32.

The end value for x > 0, of both the functions f(x) and g(x) is -∞.  

Step-by-step explanation:

The graph of f(x) shows that it is a parabola having the vertex at (10,90) and its axis is parallel to - Y-axis and also it passes through the point (0,0) point.

Therefore, the equation of f(x) is given by

(x - 10)² = - 4a (y - 90)

If it passes through (0,0) point, then (- 10)² = -4a (-90)  

⇒ a = = .

Hence, the equation becomes

⇒ .......... (1)

Now, the maximum value of f(x) for x > 0 is 90. (Answer)

Again, g(x) = x² (6 - x) ............ (2)

Hence, g'(x) = 12x - 3x² = 0 for maximum g(x) value.

⇒x = 0 or x = 4

Now, for x > 0 i.e. x = 4, g(x) = 32 is the maximum value of g(x) for x > 0. (Answer)

Now, for x approaches to +∞, then value of f(x) will approach -∞ {From equation (1)} (Answer)

And, for x approaches to +∞, then value of g(x) will approach to -∞  {From equation (2)} (Answer)

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

answer: 33 ( approx)

step-by-step explanation:

since, in the linear regression formula, the slope is the a in the equation y = b + ax ( by comparing it with the general equation of line y = mx + c )

where,

here given table is,

price ($), x   :           18         23       25       29       30       33

pairs sold, y :         16         13         10       8         6       2

so, ,   ,   ,

and   ,

thus, slop of the given line is,

⇒  

⇒   ≈ 33