Mister Exam
Graphing y = sqrt(log(0)),2*x-1
The solution
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________ f(x) = (\/ log(0) , 2*x - 1)
$$f{\left(x \right)} = \left( \sqrt{\log{\left(0 \right)}}, \ 2 x - 1\right)$$
f = (sqrt(log(0), 2*x - 1))
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:
$$\left( \sqrt{\log{\left(0 \right)}}, \ 2 x - 1\right) = 0$$
Solve this equation
Solution is not found,
it's possible that the graph doesn't intersect the axis X
so we need to solve the equation:
$$\left( \sqrt{\log{\left(0 \right)}}, \ 2 x - 1\right) = 0$$
Solve this equation
Solution is not found,
it's possible that the graph doesn't intersect the axis X
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
$$\frac{d}{d x} \left( \sqrt{\log{\left(0 \right)}}, \ 2 x - 1\right) = 0$$
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
$$\frac{d}{d x} \left( \sqrt{\log{\left(0 \right)}}, \ 2 x - 1\right) = 0$$
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
$$\frac{d^{2}}{d x^{2}} \left( \sqrt{\log{\left(0 \right)}}, \ 2 x - 1\right) = 0$$
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
$$\frac{d^{2}}{d x^{2}} \left( \sqrt{\log{\left(0 \right)}}, \ 2 x - 1\right) = 0$$
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
Limit on the left could not be calculated
$$\lim_{x \to -\infty} \left( \sqrt{\log{\left(0 \right)}}, \ 2 x - 1\right)$$
Limit on the right could not be calculated
$$\lim_{x \to \infty} \left( \sqrt{\log{\left(0 \right)}}, \ 2 x - 1\right)$$
Limit on the left could not be calculated
$$\lim_{x \to -\infty} \left( \sqrt{\log{\left(0 \right)}}, \ 2 x - 1\right)$$
Limit on the right could not be calculated
$$\lim_{x \to \infty} \left( \sqrt{\log{\left(0 \right)}}, \ 2 x - 1\right)$$