# How do you find intercepts, extrema, points of inflections, asymptotes and graph #y=2-x-x^3#?

##### 1 Answer

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#### Explanation:

To find intercepts:

x intercept means "the point where the graph cuts x-axis".At this point the y co-ordinate will be 0(the point will have form

similarly, at y intercept x=0;

now put x=0 in equation to find y intercept

and put y=0 in equation to find x intercept

from the question,

thus y intercept is at point

similarly putting y=0 we'll get x intercept(s)

for extrema and points of inflexion use derivative method

the point(s) where the first derivative of the equation is 0(or the points where the slope of curve is 0) are called critical point(s)

on differentiating

hence the curve will have no critical point

also as

the function

for points of inflexion (the point where curve changes concavity or shape) the second derivative must be 0

we have second derivative as

since,

it has no asymptotes

it will be more clear from the graph