Let f be a real-valued function defined on [0,∞), with the properties: f is continuous on [0, ∞), f(0) = 0

f ..1 exists on (0, ∞), and f ..1

0 is monotone increasing on (0,∞).

Let g be the function given by: g(x) = f(x)

for x ∈ (0, ∞).

How do I prove that g is monotone increasing on (0,∞)?

im not sure this is right

g'(x) = 6b(-5x + 1)^5 (-5)

g'(x) = -30b(-5x +1)^5

g''(x) = -30b(5)(-5x + 1)^4 (-5)

g''(x) = 750b (-5x +1)^4

g(x) = b(−5x + 1)6 − a

when

g(-x) = b(5x +1)6 - a

g'(x) = -30b(-5x +1)^5 = 0

-5x +1 = 0

x = 15

x=-7

step-by-step explanation:

x+3=-10

-10+3=-7

x=-7

irrational, then, just means all the numbers that aren't rational. every integer is a rational number, since each integer n can be written in the form n/1. however, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.

step-by-step explanation: