How do you find intercepts, extrema, points of inflections, asymptotes and graph $f(x)=(4x)/(sqrt(x^2+15))$ ?

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Answer 1 · 2017-01-16T15:01:56

No intercepts. Horizontal asymptotes : $rarr y = 4 and y =-4 larr$
Point of inflexion : O ( see the graph ),
No extrema, as $y in (-oo, oo)$ .

Use $y = f(x) = ( 4 x )/(|x| sqrt(1+15/x^2)$
If (x, y) is on the graph, so is (-x, -y), showing symmetry about O.

As $x to +-oo, y to +-4$

Cross multiply and differentiate to get the following results.

y' simplifies to $60/(x^2+15)^1.5 in (0, 4sqrt15]$

y, y and y''. vanish at O and $y''' ne 0$ , revealing O as the POI..

graph{(4x/sqrt(x^2+15)-y)(y+4)(y-4)=0 [-10, 10, -5, 5]}

How do you find intercepts, extrema, points of inflections, asymptotes and graph f(x)=(4x)/(sqrt(x^2+15))f(x)=(4x)/(sqrt(x^2+15))?