Let . Which of the following correctly identifies BOTH the interval(s) on which is…

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Let h(x)=x4−8x2h(x)=x^{4}-8x^{2}. Which of the following correctly identifies BOTH the interval(s) on which hh is concave down AND the coordinates of every point of inflection of hh? (a) Concave down on (−∞,−23)∪ ⁣(23,∞)(-\infty,-\dfrac{2}{\sqrt3})\cup\!\left(\dfrac{2}{\sqrt3},\infty\right); points of inflection at (−23,h ⁣(−23))\left(-\dfrac{2}{\sqrt3},h\!\left(-\dfrac{2}{\sqrt3}\right)\right) and (23,h ⁣(23))\left(\dfrac{2}{\sqrt3},h\!\left(\dfrac{2}{\sqrt3}\right)\right). (b) Concave down on (−43,43)\left(-\dfrac{4}{3},\dfrac{4}{3}\right); points of inflection at (−43,h ⁣(−43))\left(-\dfrac{4}{3},h\!\left(-\dfrac{4}{3}\right)\right) and (43,h ⁣(43))\left(\dfrac{4}{3},h\!\left(\dfrac{4}{3}\right)\right). (c) Concave down on (−23,23)\left(-\dfrac{2}{\sqrt3},\dfrac{2}{\sqrt3}\right); points of inflection at (−23,h ⁣(−23))\left(-\dfrac{2}{\sqrt3},h\!\left(-\dfrac{2}{\sqrt3}\right)\right) and (23,h ⁣(23))\left(\dfrac{2}{\sqrt3},h\!\left(\dfrac{2}{\sqrt3}\right)\right). (d) Concave down on (−23,∞)\left(-\dfrac{2}{\sqrt3},\infty\right); point of inflection at (23,h ⁣(23))\left(\dfrac{2}{\sqrt3},h\!\left(\dfrac{2}{\sqrt3}\right)\right) only.

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