# Help please! To investigate function by means of a derivative and to construct its schedule of f (x) =2x^3-9x^2

Gavinrandis

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Investigate function and construct its schedule of y = 2x ³ - 9x ². 1. A range of definition of function D (f) = (-∞; ∞). 2. we Determine by points of intersection function graphs with coordinate axes a) with abscissa axis : y = ⇒ 2x³ - 9x² = 0, x² (the 2nd - 9) = 0; We Have 2 roots: x = 0 and x = 9/2 = 4.5. A(0; 0); B (4.5; 0). b) with ordinate axis: x =0 ⇒ y = 0 → A(0; 04). 3. We define intervals of monotony of the Function function increases (↑) if at gt; 0, decreases (↓) if at lt; 0. y =² - 18x =6x(x-3); y + - +------------0--------------------3---------------- y ↑ max ↓ min ↑ x the =0th point of a maximum _ a move (y) = 0 x =3 point of a minimum _ min (y) = 2*3³ - 9*3² = 54 - 81 =-27. Function increases if x ∈ (-∞; 0) and x ∈ (3; ∞), decreases if x ∈ (0; 3).---4) let's determine inflection points, intervals of camber and concavity of y = (y ) = (6x² - 18x) = 12x - 18 = 6 (2x-3) . y =0 ⇒ x=3/2 =1.5 (only inflection point) Function graph convex, if y lt; 0, i.e. if x lt; 1.5, concave, if y gt; 0 ⇔ x gt; 1.5. 5. Lim y → - ∞; Lim y → ∞ x → - ∞ x → ∞

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