Let `f(x)` be differentiable function and `g(x)` be twice differentiable function. Zeros of `f(x),g^(prime)(x)` be a,b respectively, `(a

if f(x) be a twice differentiable function such that f(x) =x^(2) " for " x=1,2,3, then

Let g(x) be the inverse of an invertible function f(x) which is differentiable at x=c . Then g^(prime)(f(x)) equal. (a) f^(prime)(c) (b) 1/(f^(prime)(c)) (c) f(c) (d) none of these

If both f(x) & g(x) are differentiable functions at x=x_0 then the function defiend as h(x) =Maximum {f(x), g(x)}

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(x) is differentiable function and (f(x).g(x)) is differentiable at x = a . Then (a) g(x) must be differentiable at x=a (b.) if g(x) is discontinuous, then f(a)=0 (c.) if f(a)!=0 , then g(x) must be differentiable (d.) none of these

Let g(x) be the inverse of an invertible function f(x), which is differentiable for all real x. Then g''(f(x)) equals

Let g(x) be the inverse of an invertible function f(x), which is differentiable for all real xdot Then g''(f(x)) equals.

If f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable function and f(g(x)) is differentiable at x=a , then

If f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable function and f(g(x)) is differentiable at x=a , then

Let f(x) be a twice-differentiable function and f''(0)=2. Then evaluate lim_(xto0) (2f(x)-3f(2x)+f(4x))/(x^(2)).