Let the function `f:[-7,0]rarr R` be continuous on `[-7,0]` and differentiable on `(-7,0)` .If `f(-7)=-3` and `f'(x)<=2`, for all `x in(-7,0)`, then for all such functions `f,f(-1)+f(0)` lies in the interval

Let f(x) is a continuous function on [-7,0] and differentiable function on the interval (-7,0) such that f(-7)=-3 and given that f'(c)<=2 for c in(-7,0) .If the largest possible value of f(0) is k .Then the value of (k)/(3) is

Let f be any continuous function on [0, 2] and twice differentiable on (0, 2). If f(0) = 0, f(1) = 1 and f(2) = 2, then :

To illustrate the Mean Value Theorem with a specific function, let’s consider f(x) = x^(3) – x, a= 0, b = 2 . since f is a polynomial, it is continuous and differentiable for x, so it is certainly continuous on [0, 2] and differentiable on (0, 2) such that f(2) – f(0) = f'(c)(2 – 0)

Let f:R rarr R be twice continuously differentiable.Let f(0)=f(1)=f'(0)=0 Then

Let f be arry continuously differentiable function on [a,b] and twice differentiable on (a.b) such that f(a)=f(a)=0 and f(b)=0. Then

Let f:[2,7]rarr[0,oo) be a continuous and differentiable function.Then show that (f(7)-f(2))((f(7))^(2)+(f(2))^(2)+f(2)f(7))/(3)=5f^(2)(c)f'(c) where c in[2,7]

Let f"[2,7]rarr[0,oo) be a continuous and differentiable function. Then, the value of (f(7)-f(2))((f(7))^(2)+(f(2))^(2)+f(2).f(7))/(3) is (where c in (2,7) )

If f(x) is continuous and differentiable in x in [-7,0] and f(x) le 2 AA x in [-7,0] , also f(-7)=-3 then range of f(-1)+f(0)

Let f:R rarr R be a continuous function and f(x)=f(2x) is true AA x in R .If f(1)=3 then the value of int_(-1)^(1)f(f(x))dx is equal to (a)6(b) 0 (c) 3f(3)( d) 2f(0)