Let `f(x0` be a non-constant thrice differentiable function defined on `(-oo,oo)` such that `f(x)=f(6-x)a n df^(prime)(0)=0=f^(prime)(x)^2=f(5)dot` If `n` is the minimum number of roots of `(f^(prime)(x)^2+f^(prime)(x)f^(x)=0` in the interval [0,6], then the value of `n/2` is___

Let f(x) be a non-constant twice differentiable function defined on (-oo,oo) such that f(x)=f(1-x)a n df^(prime)(1/4)=0. Then

Let f(x) be a non-constant twice differentiable function defined on (oo,oo) such that f(x)=f(1-x) and f'(1/4)=0^(@). Then

Let f(x) be a non-constant twice differentiable function defined on (oo, oo) such that f(x) = f(1-x) and f"(1/4) = 0 . Then

Let f(x) be a non-constant twice differentiable function defined on (oo, oo) such that f(x) = f(1-x) and f"(1/4) = 0 . Then

Let f(x0 be a non-constant thrice differentiable function defined on (-oo,oo) such that f(x)=f(6-x) and f'(0)=0=f'(x)^(2)=f(5) If n is the minimum number of roots of (f'(x)^(2)+f'(x)f'''(x)=0 in the interval [0,6] then the value of (n)/(2) is

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

Let f(x) be a non-constant twice differentiable function defined on (-oo,oo) such that f(x)=f(1-x)a n df^(prime)(1/4)=0. Then f^(prime)(x) vanishes at least twice on [0,1] f^(prime)(1/2)=0 int_(-1/2)^(1/2)f(x+1/2)sinxdx=0 int_(-1/2)^(1/2)f(t)e^(sinpit)dt=int_(1/2)^1f(1-t)e^(sinpit)dt

Let f(x) be a non-constant twice differentiable function defined on (-oo,oo) such that f(x)=f(1-x)a n df^(prime)(1/4)=0. Then (a) f^(prime)(x) vanishes at least twice on [0,1] (b) f^(prime)(1/2)=0 (c) int_(-1/2)^(1/2)f(x+1/2)sinxdx=0 (d) int_(-1/2)^(1/2)f(t)e^(sinpit)dt=int_(1/2)^1f(1-t)e^(sinpit)dt

Let f(x) be a non-constant twice differentiable function defined on (-oo,oo) such that f(x)=f(1-x)a n df^(prime)(1/4)=0. Then (a) f^(prime)(x) vanishes at least twice on [0,1] (b) f^(prime)(1/2)=0 (c) int_(-1/2)^(1/2)f(x+1/2)sinxdx=0 (d) int_(-1/2)^(1/2)f(t)e^(sinpit)dt=int_(1/2)^1f(1-t)e^(sinpit)dt

Let f be a twice differentiable function such that f^(prime prime)(x)=-f(x),a n df^(prime)(x)=g(x),h(x)=[f(x)]^2+[g(x)]^2dot Find h(10)ifh(5)=11