In the Mean value theorem
`f(b)-f(a)=(b-a)f'(c),` if a=4, b=9
and f(x)=`sqrtx`, then the value of c 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, f(-1)=-18 , and f(1)=10 , what is the value of b ?

If [a b c1-a] is an idempotent matrix and f(x)=x-^2=b c=1//4 , then the value of 1//f(a) is ______.

Let f be a continuous, differentiable, and bijective function. If the tangent to y=f(x) a tx=a is also the normal to y=f(x) a tx=b , then there exists at least one c in (a , b) such that (a)f^(prime)(c)=0 (b) f^(prime)(c)>0 (c) f^(prime)(c)<0 (d) none of these

If from Largrange's mean value theorem, we have f'(x(1))=(f'(b)-f(a))/(b-a) then,

Suppose f is a real function satisfying f(x+f(x))=4f(x) and f(1)=4. Then the value of f(21) is a). 16 b). 21 c). 64 d). 105

Lagrange's mean value theorem is not applicable to f(x) in [1,4] where f(x) =

Suppose f(x) =[a+b x , x 1] and lim f(x) where x tends to 1 f(x) = f(1) then value of a and b?

The Lagrange's mean value theorem is not applicable to f(x) in [2, 4], if f(x) is

If for the function f(x)=1/4x^2+b x+10 ;f(12-x)=f(x)AAx in R , then the value of ' b ' is-