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Does $f(x)=(x-2)^frac23(2x+1)$ have Point of Inflection
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Does $$f(x)=(x-2)^frac23(2x+1)$$ have Point of Inflection
I differentiated it twice, getting
$$f''(x)=frac10(2x-5)9 (x-2)^frac43=0$$
which implies $$x=2.5$$ is Point of Inflection.
But it is unnoticeable in Graphing calculator?
algebra-precalculus differential-equations derivatives
edited Jul 29 at 3:51
max_zorn
3,15151028
asked Jul 28 at 18:30
Umesh shankar
2,20311018
add a comment |Â
up vote
2
down vote
favorite
Does $$f(x)=(x-2)^frac23(2x+1)$$ have Point of Inflection
I differentiated it twice, getting
$$f''(x)=frac10(2x-5)9 (x-2)^frac43=0$$
which implies $$x=2.5$$ is Point of Inflection.
But it is unnoticeable in Graphing calculator?
algebra-precalculus differential-equations derivatives
edited Jul 29 at 3:51
max_zorn
3,15151028
asked Jul 28 at 18:30
Umesh shankar
2,20311018
The third derivative at $x=2.5$ is not zero, so it should be noticeable with enough detail.
– Cristhian Grundmann
Jul 28 at 18:34
It isn't really noticable with DESMOS but the calculus does not lie. The second derivative changes sign at $x=2.5$
– imranfat
Jul 28 at 18:39
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Does $$f(x)=(x-2)^frac23(2x+1)$$ have Point of Inflection
I differentiated it twice, getting
$$f''(x)=frac10(2x-5)9 (x-2)^frac43=0$$
which implies $$x=2.5$$ is Point of Inflection.
But it is unnoticeable in Graphing calculator?
algebra-precalculus differential-equations derivatives
edited Jul 29 at 3:51
max_zorn
3,15151028
asked Jul 28 at 18:30
Umesh shankar
2,20311018
Does $$f(x)=(x-2)^frac23(2x+1)$$ have Point of Inflection
I differentiated it twice, getting
$$f''(x)=frac10(2x-5)9 (x-2)^frac43=0$$
which implies $$x=2.5$$ is Point of Inflection.
But it is unnoticeable in Graphing calculator?
algebra-precalculus differential-equations derivatives
edited Jul 29 at 3:51
max_zorn
3,15151028
asked Jul 28 at 18:30
Umesh shankar
2,20311018
edited Jul 29 at 3:51
max_zorn
3,15151028
edited Jul 29 at 3:51
max_zorn
3,15151028
edited Jul 29 at 3:51
max_zorn
3,15151028
3,15151028
asked Jul 28 at 18:30
Umesh shankar
2,20311018
asked Jul 28 at 18:30
Umesh shankar
2,20311018
asked Jul 28 at 18:30
Umesh shankar
2,20311018
2,20311018
The third derivative at $x=2.5$ is not zero, so it should be noticeable with enough detail.
– Cristhian Grundmann
Jul 28 at 18:34
It isn't really noticable with DESMOS but the calculus does not lie. The second derivative changes sign at $x=2.5$
– imranfat
Jul 28 at 18:39
add a comment |Â
The third derivative at $x=2.5$ is not zero, so it should be noticeable with enough detail.
– Cristhian Grundmann
Jul 28 at 18:34
It isn't really noticable with DESMOS but the calculus does not lie. The second derivative changes sign at $x=2.5$
– imranfat
Jul 28 at 18:39
The third derivative at $x=2.5$ is not zero, so it should be noticeable with enough detail.
– Cristhian Grundmann
Jul 28 at 18:34
The third derivative at $x=2.5$ is not zero, so it should be noticeable with enough detail.
– Cristhian Grundmann
Jul 28 at 18:34
It isn't really noticable with DESMOS but the calculus does not lie. The second derivative changes sign at $x=2.5$
– imranfat
Jul 28 at 18:39
It isn't really noticable with DESMOS but the calculus does not lie. The second derivative changes sign at $x=2.5$
– imranfat
Jul 28 at 18:39
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
2
down vote
As mentioned in the comments, it is difficult to notice just by looking at the graph of the second derivative, but $2.5$ really is a point of reflection, as your correctly differentiated function shows.
If you instead plot the derivative of the function, you will perhaps get more convinced even graphically (since it is clear that the first derivative is decreasing upto (approximately) $2.5$, and increasing after):
answered Jul 28 at 18:44
mickep
18.3k12149
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
As mentioned in the comments, it is difficult to notice just by looking at the graph of the second derivative, but $2.5$ really is a point of reflection, as your correctly differentiated function shows.
If you instead plot the derivative of the function, you will perhaps get more convinced even graphically (since it is clear that the first derivative is decreasing upto (approximately) $2.5$, and increasing after):
answered Jul 28 at 18:44
mickep
18.3k12149
add a comment |Â
up vote
2
down vote
As mentioned in the comments, it is difficult to notice just by looking at the graph of the second derivative, but $2.5$ really is a point of reflection, as your correctly differentiated function shows.
If you instead plot the derivative of the function, you will perhaps get more convinced even graphically (since it is clear that the first derivative is decreasing upto (approximately) $2.5$, and increasing after):
answered Jul 28 at 18:44
mickep
18.3k12149
add a comment |Â
up vote
2
down vote
up vote
2
down vote
As mentioned in the comments, it is difficult to notice just by looking at the graph of the second derivative, but $2.5$ really is a point of reflection, as your correctly differentiated function shows.
If you instead plot the derivative of the function, you will perhaps get more convinced even graphically (since it is clear that the first derivative is decreasing upto (approximately) $2.5$, and increasing after):
answered Jul 28 at 18:44
mickep
18.3k12149
As mentioned in the comments, it is difficult to notice just by looking at the graph of the second derivative, but $2.5$ really is a point of reflection, as your correctly differentiated function shows.
If you instead plot the derivative of the function, you will perhaps get more convinced even graphically (since it is clear that the first derivative is decreasing upto (approximately) $2.5$, and increasing after):
answered Jul 28 at 18:44
mickep
18.3k12149
answered Jul 28 at 18:44
mickep
18.3k12149
answered Jul 28 at 18:44
mickep
18.3k12149
answered Jul 28 at 18:44
mickep
18.3k12149
18.3k12149
add a comment |Â
add a comment |Â
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The third derivative at $x=2.5$ is not zero, so it should be noticeable with enough detail.
– Cristhian Grundmann
Jul 28 at 18:34
It isn't really noticable with DESMOS but the calculus does not lie. The second derivative changes sign at $x=2.5$
– imranfat
Jul 28 at 18:39