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

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.

Let g(x) be the inverse of an invertible function f(x) which is derivable at x=3 . If f(3)=9 and f^(prime)(3)=9 , write the value of g^(prime)(9) .

Let g(x) be the inverse of an invertible function f(x), which is differentiable for all real xdot Then g^('')(f(x)) equals. (a) -(f^('')(x))/((f^'(x))^3) (b) (f^(prime)(x)f^('')(x)-(f^(prime)(x))^3)/(f^(prime)(x)) (c) (f^(prime)(x)f^('')(x)-(f^(prime)(x))^2)/((f^(prime)(x))^2) (d) none of these

If differentiable function f(x) in inverse of g(x) then f^(g(x)) is equal to (g^(x))/((g^(prime)(x))^3) 2. 0 3. (g^(x))/((g^(prime)(x))^2) 4. 1

Let f be a continuous, differentiable, and bijective function. If the tangent to y=f(x) a tx=a is also the normal to y=f(x) a tx=b , then there exists at least one c in (a , b) such that (a)f^(prime)(c)=0 (b) f^(prime)(c)>0 (c) f^(prime)(c)<0 (d) none of these

If f(x)=|x-a|varphi(x), where varphi(x) is continuous function, then (a) f^(prime)(a^+)=varphi(a) (b) f^(prime)(a^-)=-varphi(a) (c) f^(prime)(a^+)=f^(prime)(a^-) (d) none of these

Let f be a continuous, differentiable, and bijective function. If the tangent to y=f(x)a tx=a is also the normal to y=f(x)a tx=b , then there exists at least one c in (a , b) such that f^(prime)(c)=0 (b) f^(prime)(c)>0 f^(prime)(c)<0 (d) none of these

Let y=f(x) be a parabola, having its axis parallel to the y-axis, which is touched by the line y=x at x=1. Then, (a) 2f(0)=1-f^(prime)(0) (b) f(0)+f^(prime)(0)+f^(0)=1 (c) f^(prime)(1)=1 (d) f^(prime)(0)=f^(prime)(1)

If f(x) attains a local minimum at x=c , then write the values of f^(prime)(c) and f^(prime)prime(c) .