LT

Test: Derivative fundamentals

This test introduces the derivative as a rate of change and applies the basic rules of differentiation. Tasks cover derivatives of constant, power, linear and quadratic functions.

Question qty: 10
Duration in minutes: 16
Start »

Time left: 00:00:00

Finish the test
List of tests
Start over

Sample questions

  • Differentiate f(x) = ax + (b).
  • Differentiate f(x) = ax^n.
  • For f(x) = ax² + (b)x, solve f′(x) = r.
  • f(a) = fa and f(b) = fb. Find the average rate of change on [a, b].
  • For f(x) = ax² + (b)x + (c), calculate f′(x).
  • Differentiate the constant function f(x) = c.
  • Which sum differentiation rule is correct?
  • What is the geometric meaning of a derivative at a point?

Related mathematics tests

Trigonometric identities and equations

This test applies fundamental trigonometric identities and methods for solving equations. Students write general solutions, use periodicity and select the values that belong to a specified angular interval.

Solve: Trigonometric identities and equations

Tangent and physical meaning of derivative

This test develops the geometric and physical interpretations of a derivative. Students form tangent equations, interpret velocity and acceleration and connect the sign of a derivative with the behaviour of a function.

Solve: Tangent and physical meaning of derivative

Function analysis using derivatives

This test uses the first derivative to analyse a function. Tasks include finding critical points, intervals of increase and decrease, local extrema and absolute maximum or minimum values.

Solve: Function analysis using derivatives

Optimisation problems

This test models geometric and economic optimisation situations. Students construct an objective function, determine its feasible domain, use derivatives to find an extremum and interpret the result in context.

Solve: Optimisation problems