Cusp and CornerThe graph of f(x) has a cusp at (a, 1(a)) if f(x) is continuous at 'a’ and if the followingtwo conditions hold:f (x)f (x)(i)→ ∞ as x approaches a from one side(ii)→ -00 as x approaches a from the other sideThe graph of f(x) has a corner at (a, 1(a)) if f(x) is continuous at 'a' and if the right-handand left-hand derivatives at 'a' exist and are unequal.2Consider (X) = |X| + 1 and 9X) = 1 + X'. Determine the nature of the graphs (is there acusp, corner, or neither) of f(x) and g(x) near the point (0,1).

In this question we will use basic of calculus i.e concept of continuity and differentability. We…

Answered: The graph of f(x) has a corner at (a,…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 53E

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The graph of f(x) has a corner at (a, 1(a)) if f(x) is continuous at 'a and left-hand derivatives at a' exist and are unequal.