Mister Exam
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-
How to use it?
- Graphing y =:
-
(x^2+3)/(x-1)
- 3x-x^2
- x*sin(1/x)
- xsin1/x
- Derivative of:
- 3x-6
- Integral of d{x}:
- 3x-6
-
Identical expressions
- 3x- six
- 3x minus 6
- 3x minus six
-
Similar expressions
- 2*x^2-3*x-6
- x^3-2*x^2+3*x-6
- -(x-3)*(x-6)
- 3x+6
- 4*x^2+12/3*x-6
- sqrt((((|x-1|)))*(3*x-6))+(8)/(x^(2)-4*x-21)
Graphing y = 3x-6
The solution
The graph of the function
The points of intersection with the X-axis coordinate
Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$3 x - 6 = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = 2$$
Numerical solution
$$x_{1} = 2$$
so we need to solve the equation:
$$3 x - 6 = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = 2$$
Numerical solution
$$x_{1} = 2$$
Extrema of the function
In order to find the extrema, we need to solve the equation
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
$$\frac{d}{d x} f{\left(x \right)} = $$
the first derivative
$$3 = 0$$
Solve this equation
Solutions are not found,
function may have no extrema
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
$$\frac{d}{d x} f{\left(x \right)} = $$
the first derivative
$$3 = 0$$
Solve this equation
Solutions are not found,
function may have no extrema
Inflection points
Let's find the inflection points, we'll need to solve the equation for this
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
the second derivative
$$0 = 0$$
Solve this equation
Solutions are not found,
maybe, the function has no inflections
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
the second derivative
$$0 = 0$$
Solve this equation
Solutions are not found,
maybe, the function has no inflections
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
$$\lim_{x \to -\infty}\left(3 x - 6\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(3 x - 6\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{x \to -\infty}\left(3 x - 6\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(3 x - 6\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of 3*x - 6, divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{3 x - 6}{x}\right) = 3$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = 3 x$$
$$\lim_{x \to \infty}\left(\frac{3 x - 6}{x}\right) = 3$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = 3 x$$
$$\lim_{x \to -\infty}\left(\frac{3 x - 6}{x}\right) = 3$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = 3 x$$
$$\lim_{x \to \infty}\left(\frac{3 x - 6}{x}\right) = 3$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = 3 x$$
Even and odd functions
Let's check, whether the function even or odd by using relations f = f(-x) и f = -f(-x).
So, check:
$$3 x - 6 = - 3 x - 6$$
- No
$$3 x - 6 = 3 x + 6$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$3 x - 6 = - 3 x - 6$$
- No
$$3 x - 6 = 3 x + 6$$
- No
so, the function
not is
neither even, nor odd