Answer by Narasimham for Does tangent line of inflection point always passes...
A tangent line always passes through the curve at a double or tangent point. The tangent line of inflection point always passes through the curve always, the but the center of curvature changes side...
View ArticleAnswer by Kay K. for Does tangent line of inflection point always passes...
Another way to show this isLet $l(x)$ to be the tangent line of $f(x)$ at $x=a$.Case-$1$: $f''(x<a)<0<f''(x>a)$,$$f'(x<a) < f'(a) < f'(x>a)$$$$x<a:\quad...
View ArticleAnswer by B. Goddard for Does tangent line of inflection point always passes...
Yes. Some people define inflection point as a point where the tangent line crosses the curve. But most people define it as a point where the curve changes curvature.If you think about the tangent line...
View ArticleDoes tangent line of inflection point always passes through the curve?
I saw many functions on my book and all of the tangent line of inflection point always pass through the curve, Here are examples :Example 1 :$$f(x) = x^3 \quad (x=0)$$Tangent line at $x = 0$,...
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