Math topic中文

Locating max min gc

Locating maximum and minimum points using a graphing calculator or a graphing software.

Practice questions

  1. 1A curve CC has equation y=x2−4x+4x−1y = \frac{x^2 - 4x + 4}{x - 1}. Sketch CC, stating clearly the equations of any asymptotes,…
  2. 2Sketch the graph of y=7−2x3x2+x−14y = \frac{7-2x}{3x^2 + x - 14}. Give the equations of the asymptotes and the coordinates of the tu…
  3. 3In this question, aa, bb, cc and dd are non-zero constants. The curve CC has equation y=ax2+bx−7x−cy = \frac{ax^2 + bx - 7}{x - c}…
  4. 4The function f is defined by f:x↦ex+12x+2for x∈R, x≠−1.f : x \mapsto e^x + \dfrac{1}{2x+2}\quad\text{for } x \in \mathbb{R},\ x \ne -1. A func…
  5. 5The functions f\mathrm{f} and g\mathrm{g} are defined by f:x↦2x+143x−2,x∈R,x>23,g:x↦sin⁡xx,x∈R,x>0.\begin{aligned} \mathrm{f} &: x \mapsto \frac{2x+14}{3x-2}, \quad x \in \mathbb{R}, x > \frac{2}{3}, \\ \mathrm{g} &: x \mapsto \frac{\sin x}{x}, \quad x \in \mathbb{R}, x > 0. \end{aligned}…
  6. 6A curve CC has equation y=x+9x+1y = x + \dfrac{9}{x+1}. Using differentiation, find the range of values of xx such that CC…
  7. 7The functions f\text{f} and g\text{g} are defined as follows f:x↦ln⁡(3x−2)x,x>23\text{f} : x \mapsto \frac{\ln(3x - 2)}{x}, x > \frac{2}{3}…
  8. 8The curve CC has equation given by y=1+3x−18x29x+3y = \dfrac{1+3x-18x^2}{9x+3}. Without the use of a calculator, find the range of v…
  9. 9The function f is defined by f:x↦ex+12x+2for x∈R, x≠−1.f : x \mapsto e^{x} + \dfrac{1}{2x+2}\quad\text{for } x \in \mathbb{R},\ x \ne -1. A fu…
  10. 10Trinity de Rale is a budding installation artist. Her latest mobile artwork comprises of two fixed rails placed at an an…
  11. 11A curve CC has equation y=x−3(x−2)(x+5)y = \dfrac{x-3}{(x-2)(x+5)}. Sketch CC, giving the equations of the asymptotes, the coordina…