# stationary point

• Aug 2nd 2009, 10:10 PM
furor celtica
stationary point
locate the stationary point(s) on this curve:
y=x^3 - 2lnx^3
i keep on finding (1,1), which apparently is so wrong. helpful hints?
• Aug 2nd 2009, 10:24 PM
alexmahone
Quote:

Originally Posted by furor celtica
locate the stationary point(s) on this curve:
y=x^3 - 2lnx^3
i keep on finding (1,1), which apparently is so wrong. helpful hints?

$y=x^3-2lnx^3$

$y=x^3-6lnx$

$\frac{dy}{dx}=3x^2-\frac{6}{x}$

At a stationary point,

$\frac{dy}{dx}=0$

$3x^2-\frac{6}{x}=0$

$x^2=\frac{2}{x}$

$x^3=2$

$x=2^\frac{1}{3}=1.26$

$y=x^3-2lnx^3$

$y=2-2ln2=0.61$

So the stationary point is $(1.26, 0.61)$.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8885229825973511, "perplexity": 18430.523571957663}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542938.92/warc/CC-MAIN-20161202170902-00356-ip-10-31-129-80.ec2.internal.warc.gz"}