Let `f^(prime)(x)=e^x^2 and f(0)=10.` If `A`< f(1)< B can be concluded from mean value theorem then the value of A-B will be___

If f^(prime)(x)=3x^2-2/(x^3) and f(1)=0 , find f(x) .

Let f(x)=(g(x))/x when x!=0 and f(0)=0. If g(0)=g^(prime)(0)=0 and g^ " (0)=17 then f^(prime)(0)= a). 3/4 b). -1/2 c). 17/3 d). 17/2

Let f(x)=(g(x))/x w h e nx!=0 and f(0)=0. If g(0)=g^(prime)(0)=0a n dg^(0)=17 then f'(0)= 3//4 b. -1//2 c. 17//3 d. 17//2

Suppose |[f'(x),f(x)],[f''(x),f'(x)]|=0 is continuously differentiable function with f^(prime)(x)!=0 and satisfies f(0)=1 and f'(0)=2 then (lim)_(x->0)(f(x)-1)/x is 1//2 b. 1 c. 2 d. 0

If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) for all x ,and f(0)=3, and if f(3)=3, then the value of f(-3) is ______________

If f^(prime)(1)=2 and y=f((log)_e x) , find (dy)/(dx) at x=e .

If f(0)=f(1)=0 , f^(prime)(1)=f^(prime)(0)=2 and y=f(e^x)e^(f(x)) , write the value of (dy)/(dx) at x=0 .

If f^(prime)(x)=asinx+bcosx and f^(prime)(0)=4,f(0)=3,f(pi/2)=5 . Find f(x).

If f^(prime)(x)=asinx+bcosx and f^(prime)(0)=4,\ \ f(0)=3,\ \ f(pi/2)=5 , find f(x) .

If f(x)=(log)_(x^2)(logx) , then f^(prime)(x) at x=e is (a) 0 (b) 1 (c) 1/e (d) 1/2e