Suppose f(x) is a function satisfying the following conditions :
(i) f(0)=2,f(1)=1
(ii) f has a minimum value at `x=5//2`
(iii) for all `x,f (x) = |{:(2ax,,2ax-1,,2ax+b+1),(b,,b+1,,-1),(2(ax+b),,2ax+2b+1,,2ax+b):}|`
The value of f(2) is

Suppose f(x) is a function satisfying the folowing conditions: (i)f(0)=2,f(1)=1 (ii) f(x) has a minimum value at x=(5)/(2) (iii) for all x f'(x)= |{:(2ax,2ax-1,2ax+b+1),(b,b+1,-1),(2(ax+b),2ax+2b+1,2ax+b):}| The value of f(2)+f(3) is

Suppose f(x) is a function satisfying the folowing conditions: (i)f(0)=2,f(1)=1 (ii) f(x) has a minimum value at x=(5)/(2) (iii) for all xf'(x)= |{:(2ax,2ax-1,2ax+b+1),(b,b+1,-1),(2(ax+b),2ax+2b+1,2ax+b):}| The number of solutions of the equation f(x) +1=0 is

Suppose f(x) is a function satisfying the following conditions: f(0)=2,f(1)=1 f has a minimum value at x=5/2 For all x ,f^(prime)(x)=|2a x2a x-1 2a x+b+1bb+1-1 2(a x+b)2a x+2b+1 2a x+b| where a , b are some constants. Determine the constants a , b , and the function f(x)

Suppose f(x) is a function satisfying the following conditions: f(0)=2,f(1)=1 f has a minimum value at x=5/2 For all x ,f^(prime)(x)=|2a x2a x-1 2a x+b+1bb+1-1 2(a x+b)2a x+2b+1 2a x+b| where a , b are some constants. Determine the constants a , b , and the function f(x)

If the function f(x) = axe^(bx^(2)) has maximum value at x=2 such that f(2) =1 , then find the values of a and b

f(x)={(ae^x+be^(-x),-1lexle1),(cx^2,1lexle3),(2ax+c,3lexle4):} ,f'(0)+f'(2)=e then the value of a is:

If f(x)=ax^(2)+bx+c and f(x+1)=f(x)+x+1 , then the value of (a+b) is __

If f(x) =ax^(2) + bx + c satisfies the identity f(x+1) -f(x)= 8x+ 3 for all x in R Then (a,b)=

Let lim_(xto1)(x^(a)-ax+a-1)/((x-1)^(2))=f(a) . The value of f(101) equals

If f(x)={{:(ax^(2)+1",",xgt1),(x+a",",xle1):} is derivable at x=1 , then the value of a is