The maximum possible value of (5^x - 25^x) over all real values of x is

a.0
b.1/2
c.1
d.1/4
infinity

• answer is 0..
  the maximum value of that expression is 0 when x=0.
  no other value of x gives neither infinity or any positive number.
• 12 years agoHelpfull: Yes(15) No(4)
• 5^-5-25^-5 = 0.00
  5^-4-25^-4 = 0.00
  5^-3-25^-3 = 0.01
  5^-2-25^-2 = 0.04
  5^-1-25^-1 = 0.16
  5^0-25^0 = 0.00
  5^.5-25^.5 = -2.76
  5^0.25-25^0.25 = -0.74
  5^1-25^1 = -20.00
  5^2-25^2 = -600.00
  5^3-25^3 = -15500.00
  5^4-25^4 = -390000.00
  5^5-25^5 = -9762500.00
  
  perfect ans is -1 depending on the option it would be 0
• 12 years agoHelpfull: Yes(10) No(3)
• ans 1/4....differentiate the given eq then equate to zero...we get 5^x=1/2....putting this on given eq we get..1/4
• 12 years agoHelpfull: Yes(7) No(2)
• answer is infinity
  
• 12 years agoHelpfull: Yes(2) No(5)
• answer is infinity........
• 12 years agoHelpfull: Yes(2) No(1)
• ans is not zero... the max value that i got is 1/4... if there is any other max value please do update....
• 12 years agoHelpfull: Yes(1) No(0)
• can u explain how it is infinity? @nishant
• 12 years agoHelpfull: Yes(0) No(0)
• my ans is not exactly 1/4 but taking x= -1/2 we get .247
  ans can be 1/4
• 12 years agoHelpfull: Yes(0) No(0)
• differentiating the above equation and equating it to zero
  5^xlog5-2*25^xlog5=0
  5^x=2*25^2x
  x=-0.43
  by sub x in the equ we get max value as 0.25
• 12 years agoHelpfull: Yes(0) No(1)