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GETTING STARTED WITH GRAPHS

GETTING STARTED WITH GRAPHS

GETTING STARTED WITH GRAPHS

FUNCTIONS

GRAPH OF INVERSE TRIGONOMETRIC FUNCTIONS

The graph of the second derivation f”(x) is given in the following figure. State the x – coordinate of the point of inflection of f. Given reasons for your answer.

Following is the graph of y = f’ (x) , given that f(c) = 0. Analyse the graph and answer the following questions.

(a) How many times the graph of y = f(x) will intersect the x – axis?

(b) Discuss the type of roots of the equation f (x) = 0, a≤x≤b.

(c) How many points of inflection the graph of y=f(x),a≤x≤b, has?

(d) Find the points of local maxima/minima ofy=f(x),a<xb.

(e) How many roots equation f”(x)=0 has?

In the following graph, state the absolute and local maximum and minimum values of the function.

Let f(x)=x2−2x−1∀x∈R.Letf:(−∞,a]→[b,∞), where a is the largest real number for which f(x) is bijective.

If f:R→R, then range of values of k for which equation f(|x|)=k has 4 distinct real roots is

Draw the graph of y=tan−1x+cot−1x

The graph of the derivative f'(x) is given in the following figure.

(b) Find the values of x for which f has local maximum or minimum.

(c) Find the intervals in which f is concave upward or downward.

(d) Find the point of inflection.

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The graph of the derivative f'(x) is given in the following figure.

(a) Find the interval in which f is increasing or decreasing.

(b) Find the values of x for which f has local maximum or minimum.

(c) Find the intervals in which f is concave upward or downward.

(c) Find the point of inflection.

In the given figure (not to scale), O is the centre of the circle. A,B,C and D are concyclic and AB=CD . If /_MON =120^(@) , then find /_ OPN .

Determine the point of symmetry of a regular hexagon.

Match the following Column A to Column B

Find the area of figure given below.

Find the perimeter of the figure given below.

Find the area of the figure given below.

The inequation represented by the graph given below is :

The inequation that best describes the graph given below is _________