Mister Exam

Other calculators

Plotting a function graph/ 89x+58sin(x)+85

Graphing y = 89x+58sin(x)+85

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
f(x) = 89*x + 58*sin(x) + 85
f(x)=(89x+58sin⁡(x))+85f{\left(x \right)} = \left(89 x + 58 \sin{\left(x \right)}\right) + 85 
f = 89*x + 58*sin(x) + 85
The graph of the function
02468-8-6-4-2-1010-20002000
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:
(89x+58sin⁡(x))+85=0\left(89 x + 58 \sin{\left(x \right)}\right) + 85 = 0
Solve this equation
The points of intersection with the axis X:

Numerical solution
x1=−0.591611598965212x_{1} = -0.591611598965212
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to 89*x + 58*sin(x) + 85.
(0⋅89+58sin⁡(0))+85\left(0 \cdot 89 + 58 \sin{\left(0 \right)}\right) + 85
The result:
f(0)=85f{\left(0 \right)} = 85
The point:
(0, 85)
Extrema of the function
In order to find the extrema, we need to solve the equation
ddxf(x)=0\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:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
the first derivative
58cos⁡(x)+89=058 \cos{\left(x \right)} + 89 = 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
d2dx2f(x)=0\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:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
the second derivative
−58sin⁡(x)=0- 58 \sin{\left(x \right)} = 0
Solve this equation
The roots of this equation
x1=0x_{1} = 0
x2=πx_{2} = \pi

Сonvexity and concavity intervals:
Let’s find the intervals where the function is convex or concave, for this look at the behaviour of the function at the inflection points:
Concave at the intervals
(−∞,0]∪[π,∞)\left(-\infty, 0\right] \cup \left[\pi, \infty\right)
Convex at the intervals
[0,π]\left[0, \pi\right]
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
lim⁡x→−∞((89x+58sin⁡(x))+85)=−∞\lim_{x \to -\infty}\left(\left(89 x + 58 \sin{\left(x \right)}\right) + 85\right) = -\infty
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
lim⁡x→∞((89x+58sin⁡(x))+85)=∞\lim_{x \to \infty}\left(\left(89 x + 58 \sin{\left(x \right)}\right) + 85\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 89*x + 58*sin(x) + 85, divided by x at x->+oo and x ->-oo
lim⁡x→−∞((89x+58sin⁡(x))+85x)=89\lim_{x \to -\infty}\left(\frac{\left(89 x + 58 \sin{\left(x \right)}\right) + 85}{x}\right) = 89
Let's take the limit
so,
inclined asymptote equation on the left:
y=89xy = 89 x
lim⁡x→∞((89x+58sin⁡(x))+85x)=89\lim_{x \to \infty}\left(\frac{\left(89 x + 58 \sin{\left(x \right)}\right) + 85}{x}\right) = 89
Let's take the limit
so,
inclined asymptote equation on the right:
y=89xy = 89 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:
(89x+58sin⁡(x))+85=−89x−58sin⁡(x)+85\left(89 x + 58 \sin{\left(x \right)}\right) + 85 = - 89 x - 58 \sin{\left(x \right)} + 85
- No
(89x+58sin⁡(x))+85=89x+58sin⁡(x)−85\left(89 x + 58 \sin{\left(x \right)}\right) + 85 = 89 x + 58 \sin{\left(x \right)} - 85
- No
so, the function
not is
neither even, nor odd
    © Mister Exam – Calculator