#function properties

General Mathematics 4

If y = t(x) be a differentiable function ∀ x ∈ ℝ, then which of the following is always true?

Simply put, complete solution: write formula, plug data, do arithmetic. Final value matches d²y/dx² + (dy/dx)³ d²x/dy² = 0. Simple and accurate.

Ref: NCERT Mathematics Class XI and XII

View Details

General Mathematics 4

The function f (x) = x³ has a

Understanding this is easy: using formula we get point of inflexion at = 0. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get point of inflexion at = 0.

Ref: NCERT Mathematics Class XI and XII

View Details

General Mathematics 1

Consider the function f(x) = x + 1/x . Which of the following is correct?

We know that using formula we get fmax < fmin. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get fmax < fmin.

Ref: NCERT Mathematics Class XI and XII

View Details

Sets, Relations and Functions

Let N be the set of natural numbers and f : N → N be a function given by f (x) = x + 1 ∀ x ∈ N. Which one of the followi

We can see that solving fully: apply relevant formula, put numbers, compute. Result comes as f is one - one but not onto. Easy verification shows it satisfies condition.

Ref: NCERT Mathematics Class XI — Sets, Relations and Functions

View Details