[" If "f(x)" is continuous on "[0,2]," differentiable on "(0,2),f(0)=2,f(2)=8," and "f'(x)<=3" for all "x" in "],[(0,2)," then find the value of "f(1)" ."]

If f(x) is continuous on [0,2] , differentiable in (0,2) ,f(0)=2, f(2)=8 and f'(x) le 3 for all x in (0,2) , then find the value of f(1) .

If f (x) is continous on [0,2], differentiable in (0,2) f (0) =2, f(2)=8 and f '(x) le 3 for all x in (0,2), then find the value of f (1).

If f (x) is continous on [0,2], differentiable in (0,2) f (0) =2, f(2)=8 and f '(x) le 3 for all x in (0,2), then find the value of f (1).

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:[0,2]vecR be a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1 L e t :F(x)=int_0^(x^2)f(sqrt(t))dt for x in [0,2] . If F^(prime)(x)=f^(prime)(x) . for all x in (0,2), then F(2) equals

Let f:[0,2]to RR be a function which is continuous on [0,2] and is differentiable on (0, 2) with f(0)=1 . Let F(x)=int_(0)^(x^(2))f(sqrt(t))dt" for "x in[0,2] . If F'(x)=f'(x) for all x in(0,2) , the F(2) equals

Let f : [0,2] rarr R be a function which is continuous on [0 , 2] and is differentiable on (0 , 2) with f(0) = 1. Let F(x) = int_0^(x^2) f(sqrtt)dt for x in [0,2] . If F'(x) = f'(x) for all x in (0,2) , then F(2) equals