If the functions `f (x) and phi(x)` are continuous in `[a,b]` and differentiable in `(a,b),` then the value of `'c'` for the pair of functions `f(x) =e^x, phi(x) = e^-x` is

If the function f(x) and phi (x) are continuous in [a,b] and differentiable in (a,b) , then the value of 'c' for the pair of functions f(x) = e^(x), phi (x) = e^(-x) is

If the functions f(x) and phi(x) are continuous in [a,b] and differentiable in (a,b), then the value of c'c' 'for the pair of functions f(x)=e^(x),phi(x)=e^(-x) is

If the functions f(x) and phi(x) are continuous in [a,b] and differentiable in (a,b), then the value of 'c' for the pair of functions f(x)=sqrt(x),phi(x)=(1)/(sqrt(x)) is

if the functions f(x) and phi (x ) are continuous in [a,b] and differentiable in (a,b) , then the value of 'c' for the pair of function f (x) = sqrt(x ) , phi (x) = ( 1)/( sqrt(x)) is

If f(x)={x,x 1 find b and c if function is continuous and differentiable at x=1

Let f(x) be a function such that its derovative f'(x) is continuous in [a, b] and differentiable in (a, b). Consider a function phi(x)=f(b)-f(x)-(b-x)f'(x)-(b-x)^(2) A. If Rolle's theorem is applicable to phi(x) on, [a,b], answer following questions. If there exists some unmber c(a lt c lt b) such that phi'(c)=0 and f(b)=f(a)+(b-a)f'(a)+lambda(b-a)^(2)f''(c) , then lambda is