Question

Please help.i need to turn in tonight.
Thank you very much in advance.

Answer 1

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 =
`(100)/(360)` =
`(5)/(18)`.

Hence, the equation becomes
`(x-10)^(2)=-(10)/(9)  (y-90)`

⇒
`y= 90-(9)/(10) (x-10)^(2)` .......... (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)