If graph of `y=f(x)` is symmetrical about the point `(5,0)` and `f^(prime)(7)=3,` then the value of `f^(prime)(3)` is__________

The graph of the function y= f (x) is symmetrical about the line x=2 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 graph of y=f(x) is symmetrical about the y-axis and that of y=g(x) is symmetrical about the origin and if h(x)=f(x)dotg(x),t h e n(d^3h(x))/(dx^3)a tx=0 is (a)cannot be determined (b) f(0)dotg(0) (c)0 (d) none of these

If function f satisfies the relation f(x)xf^(prime)(-x)=f(-x)xf^(prime)(x)fora l lx ,a n df(0)=3,a n diff(3)=3, then the value of f(-3) is ______________

Consider the polynomial f(x)=a x^2+b x+cdot If f(0),f(2)=2, then the minimum value of int_0^2|f^(prime)(x)dxi s___

If f(x) is a real-valued function defined as f(x)=In (1-sinx), then the graph of f(x) is (A) symmetric about the line x =pi (B) symmetric about the y-axis (C) symmetric and the line x=(pi)/(2) (D) symmetric about the origin

If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

f^(prime)(x)=phi(x) and phi^(prime)(x)=f(x) for all x.Also,f(3)=5 and f^(prime)(3)=4 . Then the value of [f(10)]^2-[phi(10)]^2 is _____

Let f(x) be a polynomial of degree 3 such that f(3)=1,f^(prime)(3)=-1,f^('')(3)=0,a n df^(''')(3)=12. Then the value of f^(prime)(1) is (a) 12 (b) 23 (c) -13 (d) none of these

The function f: RvecR satisfies f(x^2)dotf^(x)=f^(prime)(x)dotf^(prime)(x^2) for all real xdot Given that f(1)=1 and f^(1)=8 , then the value of f^(prime)(1)+f^(1) is 2 b. 4 c. 6 d. 8