Def1. 如果函数 f一直位于其定义域I内切线的上方,那么函数称为上凸的(concave upward),如果一直位于下方,就称为下凸的(concave downward)凹凸性测试(Concavity Test)如果一个函数在区间I上f''(x)>0,…
As with concave up, the upside down “U” in a concave down graph can also be flattened, scrunched, or stretched. Defining Concave Up or Down with Tangent Lines Analytically, a concave up graph can be defined by itstangent line; Take a point where the graph has a low point: the tangen...
critical point(极值点):f'(x) = 0 的点,f'(x)>0 上升, f'(x) < 0 下降 inflection point(扭转点): f''(x) = 0 的点,f''(x) > 0 concave up or concave down 这里的中英文很让人迷惑,还是自己记住吧: Concave up: the slope increases. Concave down: the slope decreases: 画图一般分...
CalculusDerivatives can help! The derivative of a function gives the slope.When the slope continually increases, the function is concave upward. When the slope continually decreases, the function is concave downward.Taking the second derivative actually tells us if the slope continually increases or ...
Curves that are concave up look like an upright bowl, curves that are concave down look like an upside-down bowl. In the simplest terms, it could also be like describing a smile and a frown. Image of a concave up curve and a concave down curve. In calculus, concavity is defined as ...
Concave down: y=f(x) is concave down on an interval I iff d2ydx2<0 in the interval I. Point of inflection: The point at which curve changes its concavity from either concave up to concave down or concave down to concave up, that is called poin...
Learn the concave function in mathematics. Study the uses of the concave function with examples. Compare the concave up vs. concave down functions...
Learn about when a function is concave up or concave down. Discover how to algebraically determine if a function is concave up, and how to graph a...
Answer to: Determine the intervals on which the function is concave up or concave down. f ( x ) = \frac { 4 x } { ( 4 x ) ^ { 2 } + 27 } By...
Expert Help in Algebra/Trig/(Pre)calculus to Guarantee Success in 2018 See tutors like this If f(x)=(x-3)/(x^2) then we can observe that there's a vertical asymptote, x=0.f'(x) = (-x2 + 6x) / x4 and the domain of f' also excludes 0.f...