Let `g(x)=f(x)sinx ,w h e r ef(x)` is a twice differentiable function on `(-oo,oo)` such that `f'(-pi)=1.` The value of `|g^''(-pi)|` equals __________

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) is an odd differentiable function defined on (-oo,oo) such that f'(3)=2 , then f'(-3) equal to

IF f(x) is an odd differentiable function defined on (-oo, oo) such that f'(3) = 2, then f'(-3) equal to

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 (a) f'(x) vanishes at least twice on [0,1] (b) f'(1/2)=0 (c) ∫_{-1/2}^{1/2}f(x+1/2)sinxdx=0 (d) ∫_{0}^{1/2}f(t)e^sinxtdt=∫_{1/2}^{1}f(1−t)e^sinπtdt

Examine the differentiability of the function f(x)=|sinx-cosx| at x=(pi)/(4) .

Prove that the curves y=f(x),[f(x)>0],a n dy=f(x)sinx ,w h e r ef(x) is differentiable function, have common tangents at common points.

If f is a twice differentiable function such that f''(x)=-f(x),f'(x)=g(x) ,h(x)=[f(x)]^2+[g(x)]^2 if h(5)=11, then h(10) equals

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1) =1 , then

Let f:(0,oo)toRR be a differentiable function such that f'(x)=2-(f(x))/(x) for all x in(0,oo) and f(1)ne1 . Then-

Let f(x) = x + cos x + 2 and g(x) be the inverse function of f(x), then g'(3) equals _