Mister Exam

The maximum value of the function

v

Graph Limits:

from to

Intersection points:

does show?

Piecewise:

    What can it do?

    • Plot the graph around the maximum
    • Finds all points where the function has maximum values in local regions

    Examples of functions with critical points

    • Inverse quadratic function
    • -x^2
    • Absolute function with negative coefficient
    • -|x|
    • Sine function
    • sin(x)
    • Logarithmic function with the negative argument
    • -ln(x)
    • Parabola with the negative linear coefficient
    • -x^2 + 4*x + 4

    Learn more about Curve sketching.

    The above examples also contain:

    • the modulus or absolute value: absolute(x) or |x|
    • square roots sqrt(x),
      cubic roots cbrt(x)
    • trigonometric functions:
      sinus sin(x), cosine cos(x), tangent tan(x), cotangent ctan(x)
    • exponential functions and exponents exp(x)
    • inverse trigonometric functions:
      arcsine asin(x), arccosine acos(x), arctangent atan(x), arccotangent acot(x)
    • natural logarithms ln(x),
      decimal logarithms log(x)
    • hyperbolic functions:
      hyperbolic sine sh(x), hyperbolic cosine ch(x), hyperbolic tangent and cotangent tanh(x), ctanh(x)
    • inverse hyperbolic functions:
      hyperbolic arcsine asinh(x), hyperbolic arccosinus acosh(x), hyperbolic arctangent atanh(x), hyperbolic arccotangent acoth(x)
    • other trigonometry and hyperbolic functions:
      secant sec(x), cosecant csc(x), arcsecant asec(x), arccosecant acsc(x), hyperbolic secant sech(x), hyperbolic cosecant csch(x), hyperbolic arcsecant asech(x), hyperbolic arccosecant acsch(x)
    • rounding functions:
      round down floor(x), round up ceiling(x)
    • the sign of a number:
      sign(x)
    • for probability theory:
      the error function erf(x) (integral of probability), Laplace function laplace(x)
    • Factorial of x:
      x! or factorial(x)
    • Gamma function gamma(x)
    • Lambert's function LambertW(x)
    • Trigonometric integrals: Si(x), Ci(x), Shi(x), Chi(x)

    The insertion rules

    The following operations can be performed

    2*x
    - multiplication
    3/x
    - division
    x^2
    - squaring
    x^3
    - cubing
    x^5
    - raising to the power
    x + 7
    - addition
    x - 6
    - subtraction
    Real numbers
    insert as 7.5, no 7,5

    Constants

    pi
    - number Pi
    e
    - the base of natural logarithm
    i
    - complex number
    oo
    - symbol of infinity