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Calculus Question? 5 star best answer?
F(x)=4(x+1)^(2/5)/(x^2-x-6)
A. At what points is the function discontinuous? Give Reasons.
B. At what points is the function non-differentiable? Give Reasons for your answers.
For part A. I had at (-1,0) the function is discontinuous because of a vertical tangent. Was there any other points of discontinuity?
And part b I didn't understand.
Thanks in advance
3 Answers
- Mr NLv 58 years agoFavorite Answer
Having a vertical tangent doesn't mean discontinuity.. Having a vertical asymptote does
And this function is continuous everywhere except at 3 and -2 (the roots of the denominator) where it has vertical asymptotes
Having a vertical tangent/asymptote means non-differentiability..
The function is smooth (differentiable) everywhere except at 3 and -2 where it has vertical asymptotes
F'(x) i.e. the derivative of F(x) is defined everywhere except at 3 and -2, which are thus the only points of non-differentiabilities
- Anonymous8 years ago
the function is not defined when the denominater equals zero....
In the question the denominator will be zero at the roots of the quad expression (x^2-x-6) i.e, -2 and +3.... So if u plot a graph u cannot get y coordinate at these points ,therefore the function is discontinuous at -2 and 3......
And for differentiability ,the function is defferentiable only if it is continuous..... So the function is also not differentiable at -2 and 3
