Mister Exam
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-
How to use it?
- Graphing y =:
- x^3/2(x+1)^2
- (x^2+5)/(x-3)
- x^2+4x-1
- x^3+6x^2+9x
- Integral of d{x}:
-
6x-2
- Derivative of:
-
6x-2
-
Identical expressions
- 6x- two
- 6x minus 2
- 6x minus two
-
Similar expressions
- (x^2+3)^2-6*(x-2)^2+5*x^2
- 6x+2
- x^3/3-5/2*x^2+6*x-2
- (6e^(x-2)-3x^2+4x+2(x-2))+16(3cos^2(x-2)sin^2(x-2)+cos^4(x-2))/(cos^6(x-2))-2
Graphing y = 6x-2
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:
$$6 x - 2 = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = \frac{1}{3}$$
Numerical solution
$$x_{1} = 0.333333333333333$$
so we need to solve the equation:
$$6 x - 2 = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = \frac{1}{3}$$
Numerical solution
$$x_{1} = 0.333333333333333$$
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
$$6 = 0$$
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
$$6 = 0$$
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
$$\lim_{x \to -\infty}\left(6 x - 2\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(6 x - 2\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{x \to -\infty}\left(6 x - 2\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(6 x - 2\right) = \infty$$
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 6*x - 2, divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{6 x - 2}{x}\right) = 6$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = 6 x$$
$$\lim_{x \to \infty}\left(\frac{6 x - 2}{x}\right) = 6$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = 6 x$$
$$\lim_{x \to -\infty}\left(\frac{6 x - 2}{x}\right) = 6$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = 6 x$$
$$\lim_{x \to \infty}\left(\frac{6 x - 2}{x}\right) = 6$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = 6 x$$
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:
$$6 x - 2 = - 6 x - 2$$
- No
$$6 x - 2 = 6 x + 2$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$6 x - 2 = - 6 x - 2$$
- No
$$6 x - 2 = 6 x + 2$$
- No
so, the function
not is
neither even, nor odd