Let `Q(x)=f(x)+f(1-x) and f^(primeprime)(x)<0, 0lt=xlt=1` then

Let g(x)=2f(x/2)+f(1-x) and f^(primeprime)(x)<0 in 0<=x<=1 then g(x)

Let f(0)=f'(0)=0 and f^(primeprime)(x)=sec^4x+4 then find f(x)

A nonzero polynomial with real coefficient has the property that f(x)=f^(prime)(x)dot f^(primeprime)(x)dot If a is the leading coefficient of f(x), then the value of 1/(2a) is____

A nonzero polynomial with real coefficient has the property that f(x)=f^(prime)(x)dot f^(primeprime)(x)dot If a is the leading coefficient of f(x), then the value of 1/(2a) is____

A nonzero polynomial with real coefficient has the property that f(x)=f^(prime)(x)dot f^(primeprime)(x)dot If a is the leading coefficient of f(x), then the value of 1/(2a) is____

If F(x)=f(x)dotg(x) and f^(prime)(x)dotg^(prime)(x)=c , prove that (F^(primeprime))/F=f^(primeprime)/f+g^(primeprime)/g+(2c)/(fg)&F^(primeprimeprime)/F=f^(primeprimeprime)/f+g^(primeprimeprime)/g

A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n (a) f^(primeprime)(x)=f(x)=0 (b) 4f^(primeprime)(x)+f(x)=0 (c) f^(primeprime)(x)+f(x)=0 (d) 4f^(primeprime)(x)-f(x)=0

A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n (a) f^(primeprime)(x)=f(x)=0 (b) 4f^(primeprime)(x)+f(x)=0 (c) f^(primeprime)(x)+f(x)=0 (d) 4f^(primeprime)(x)-f(x)=0

If F(x)=f(x)dotg(x) and f^(prime)(x)dotg^(prime)(x)=c , prove that (F")/F=f^(primeprime)/f+g^(primeprime)/g+(2c)/(fg)&F^(primeprimeprime)/F=f^(primeprimeprime)/f+g^(primeprimeprime)/g

Let Q(x)=f(x)+f(1-x) and f'(x)<0,0<=x<=