Given `f(0)=0;f^(prime)(0)=0 and f^(prime prime)(x)=sec^2x+sec^2xtan^2x+4` then `f(x)=`

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 .

Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are differentiable functions. At some point x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)=4f(x_0),g^(prime)(x_0)=-7g(x_0), and h^(prime)(x_0)=kh(x_0), then the value of k is

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 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

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

If f(x)=m x+ca n df(0)=f^(prime)(0)=1. What is f(2)?

If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that f(0)=10 ,g(0)=2,f(1)=2,g(1)=4, then in the interval (0,1)dot (a) f^(prime)(x)=0fora l lx (b) f^(prime)(x)+4g^(prime)(x)=0 for at least one x (c) f(x)=2g'(x) for at most one x (d)none of these

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

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