continuity and differentiability

The following theorem say 'Differentiability implies continuity..

Introduction to Differentiation - After having studied functions, limits and continuity in the previous chapter, we shall further divide the class of continuous functions into two sub classes, derivable and non-derivable.After having studied functions, limits and ..

The graph of a continuous, differentiable function is given. Which one of the following can be the graph of f ′ ( x )? => Graph A or Graph B or Graph C or Graph D..

Which of the following is correct for a continuous and twice differentiable function f ( x )? => At the point of inflection, the concavity of the curve f ( x ) changes or At the point of inflection, the concavity of the curve f ( x ) does not change or At the point of inflection..

Conclusion - In this chapter, we have studied various types of functions and their graphs. The use of graphs also facilitate the study of domain and range of functions.In this chapter, we have studied various types of functions and their graphs. The use of graphs also facilitate the study of domain..

f ( x ) is a continuous, twice differentiable function. The graph of f ″ ( x ) is given. Which one of the following is true in the case of f ( x ) ? => f ( x ) is concave downward in (0, ∞) or f ( x ) is concave upw..

The graph of a continuous and twice differentiable function f ( x ) is shown . Which of the following can be the graph of its first derivative f ′ ( x )? => Graph A or Graph B or Graph C or Graph D..

f ( x ) is a continuous, differentiable function. The graph of f ′ ( x ) is given below. Which one of the following is true in the case of f ( x ) ? => f ( x ) increases in (-∞,0) or f ( x ) increases in (0, ∞) ..

f ( x ) is a continuous, differentiable function. The graph of f ′ ( x ) is given. Which one of the following is true in the case of f ( x )? => f ( x ) decreases in (- ∞,∞) or f ( x ) has critical po..

f ( x ) is a continuous, differentiable function. The graph of f ′( x ) is given . Which one of the following is true in the case of f ( x )? => f ( x ) decreases in(-∞,-1) ∪ (0, 1) ∪ (1, 2) or f ( x ..