Graphing functions using derivatives

MathProblemsBank banner

MathProblemsBank banner

Math Problems and solutions

Problem list Free problems

Attention! If a subsection is selected, then the search will be performed in it!

Problem: Examine the function by methods of differential calculus and plot the graph: \[ f(x)=(x-1)^{2}(x+1)^{2} \text {. } \]

2.4.1 Graphing functions using derivatives

2.54 $

Problem: Examine the function by methods of differential calculus and plot the graph: \[ f(x)=\frac{x^{3}}{x^{2}+1} \text {. } \]

2.4.2 Graphing functions using derivatives

2.54 $

Problem: Examine the function by methods of differential calculus and plot the graph: \[ f(x)=x^{2} e^{x} \text {. } \]

2.4.3 Graphing functions using derivatives

2.54 $

Problem: Examine the function by methods of differential calculus and plot the graph: \[ f(x)=x+\ln x \text {. } \]

2.4.4 Graphing functions using derivatives

2.54 $

Problem: Examine the function by methods of differential calculus and plot the graph: \[ y=\frac{-2 x^{3}-x^{2}+2 x+3}{x^{2}-2 x-3} . \]

2.4.5 Graphing functions using derivatives

2.54 $

Problem: Examine the function, given by the parametric equations, in accordance with the given scheme. Plot its graph. \[ \begin{array}{l} f(t)=t^{3}-3 t, \quad g(t)=-3 t^{3}-4 t^{2}+t \\ \left\{\begin{array}{l} x=f(t) \\ y=g(t) \end{array}-\infty

2.4.6 Graphing functions using derivatives

6.35 $

Problem: Investigate the function by methods of differential calculus and plot the graph: \[ y=x e^{-x^{2}} \text {. } \]

2.4.7 Graphing functions using derivatives

2.54 $

Problem: Conduct a complete examination of the function by methods of differential calculus and plot the graph: \[ y=\frac{x^{2}-6 x+10}{x-3} \text {. } \]

2.4.8 Graphing functions using derivatives

2.54 $

Problem: Conduct a complete examination of the function by methods of differential calculus and plot the graph. \[ y=\frac{x^{3}-4}{x^{2}} \text {. } \]

2.4.9 Graphing functions using derivatives

2.54 $

Problem: Conduct a complete examination of the function by methods of differential calculus and plot the graph: \[ y=\frac{x^{2}-4 x+1}{x-4} . \]

2.4.10 Graphing functions using derivatives

2.54 $

Problem: Conduct a complete examination of the function by methods of differential calculus and plot the graph: \[ y=\sqrt[3]{(x-1)(x+2)^{2}} . \]

2.4.11 Graphing functions using derivatives

2.54 $

Problem: Conduct a complete examination of the function by methods of differential calculus and plot the graph: \[ y=-\frac{e^{-(x+2)}}{x+2} \]

2.4.12 Graphing functions using derivatives

2.54 $