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

If y=f(x) is an odd differentiable function defined on (-oo,oo) such that f^(prime)(3)=-2,t h e n|f^(prime)(-3)| equals_________.

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 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

Let f: RvecR be a one-one onto differentiable function, such that f(2)=1a n df^(prime)(2)=3. The find the value of ((d/(dx)(f^(-1)(x))))_(x=1)

Let f: RvecR be a one-one onto differentiable function, such that f(2)=1a n df^(prime)(2)=3. The find the value of ((d/(dx)(f^(-1)(x))))_(x=1)

If is a real valued function defined by f(x)=x^2+4x+3, then find f^(prime)(1)a n df^(prime)(3)dot

If f(x)=|logx|,xgt0 ,find f^(prime)(1/e)a n df^(prime)(e)