List of top Mathematics Questions on Second Order Derivatives

If \(x = e^{y+e^y+.... to \space ∞}, x> 0\) then \(\frac{d^2y}{dx^2}\) is:

If f(x) is a function which is derivable in an interval 1 containing a point c, then match List I with List II.

List I		List II
A.	f(x) has second order derivate at x = c such that f'(c) = 0 and f'(c) < 0; then	I.	point of inflexion of f(x)
B.	Necessary condition for point x = c to be extreme point of f(x) is	II.	‘c’ is point of local minima of f(x)
C.	If f'(x) does not change its sign as x crosses the point x = c then it is called a	III.	c is a critical point of f(x)
D.	f(x) has second order derivate at x = c such that f'(c) and f'(c) > 0; then	IV.	‘c’ is point of local maxima of f(x)

Choose the correct answer from the options given below :

If x=5t and \(y=\frac5t,\) then \(\frac{d^2y}{dx^2}\) at t=1 is

If \(y=x^3\log x, then\ \frac{d^2y}{dx^2}\) is:

If x = 4t², \(y=\frac{3}{t^3}\), then \(\frac{d^2y}{dx^2}\) at t = 1 is :

If \(x = \frac{1}{t^2}\) and \(y =\frac{1}{t^3}\), then \(\frac{d^2y}{dx^2}\) at \(t=1\) is: