Let `f^(prime)(x)=e^x^2 and f(0)=10.`
If A

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

Let f((x+y)/2)=(f(x)+f(y))/2fora l lr e a lxa n dy If f^(prime)(0) exists and equals -1a n df(0)=1,t h e n f i n d f(2)dot

If f(x)=|x a a a x a a a x|=0, then f^(prime)(x)=0a n df^(x)=0 has common root f^(x)=0a n df^(prime)(x)=0 has common root sum of roots of f(x)=0 is -3a none of these

Let f(x)=(e^(x))/(1+x^(2)) and g(x)=f'(x) , then

Let f: R->R be a differentiable function with f(0)=1 and satisfying the equation f(x+y)=f(x)f^(prime)(y)+f^(prime)(x)f(y) for all x ,\ y in R . Then, the value of (log)_e(f(4)) is _______

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

Let f(x^m y^n)=mf(x)+nf(y) for all x , y in R^+ and for all m ,n in Rdot If f^(prime)(x) exists and has the value e/x , then find (lim)_(xvec0)(f(1+x))/x

If a function f(x) has f^(prime)(a)=0a n df^(a)=0, then x=a is a maximum for f(x) x=a is a minimum for f(x) it is difficult to say (a)a n d(b) f(x) is necessarily a constant function.

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2a n dy(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

y=f(x) is a function which satisfies (i) f(0)=0 (ii) f^prime prime(x)=f^prime(x) and (iii) f^prime(0)=1 then the area bounded by the graph of y=f(x) , the lines x=0, x-1=0 and y +1=0 , is