Mister Exam

Other calculators

Plotting a function graph/ 12*sin(x)-17*x+8

Graphing y = 12*sin(x)-17*x+8

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
f(x) = 12*sin(x) - 17*x + 8
f(x)=(−17x+12sin⁡(x))+8f{\left(x \right)} = \left(- 17 x + 12 \sin{\left(x \right)}\right) + 8 
f = -17*x + 12*sin(x) + 8
The graph of the function
-4.5-4.0-3.5-3.0-2.5-2.0-1.5-1.0-0.50.00200
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:
(−17x+12sin⁡(x))+8=0\left(- 17 x + 12 \sin{\left(x \right)}\right) + 8 = 0
Solve this equation
The points of intersection with the axis X:

Numerical solution
x1=1.09952297575982x_{1} = 1.09952297575982
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to 12*sin(x) - 17*x + 8.
(12sin⁡(0)−0)+8\left(12 \sin{\left(0 \right)} - 0\right) + 8
The result:
f(0)=8f{\left(0 \right)} = 8
The point:
(0, 8)
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
12cos⁡(x)−17=012 \cos{\left(x \right)} - 17 = 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
−12sin⁡(x)=0- 12 \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→−∞((−17x+12sin⁡(x))+8)=∞\lim_{x \to -\infty}\left(\left(- 17 x + 12 \sin{\left(x \right)}\right) + 8\right) = \infty
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
lim⁡x→∞((−17x+12sin⁡(x))+8)=−∞\lim_{x \to \infty}\left(\left(- 17 x + 12 \sin{\left(x \right)}\right) + 8\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 12*sin(x) - 17*x + 8, divided by x at x->+oo and x ->-oo
lim⁡x→−∞((−17x+12sin⁡(x))+8x)=−17\lim_{x \to -\infty}\left(\frac{\left(- 17 x + 12 \sin{\left(x \right)}\right) + 8}{x}\right) = -17
Let's take the limit
so,
inclined asymptote equation on the left:
y=−17xy = - 17 x
lim⁡x→∞((−17x+12sin⁡(x))+8x)=−17\lim_{x \to \infty}\left(\frac{\left(- 17 x + 12 \sin{\left(x \right)}\right) + 8}{x}\right) = -17
Let's take the limit
so,
inclined asymptote equation on the right:
y=−17xy = - 17 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:
(−17x+12sin⁡(x))+8=17x−12sin⁡(x)+8\left(- 17 x + 12 \sin{\left(x \right)}\right) + 8 = 17 x - 12 \sin{\left(x \right)} + 8
- No
(−17x+12sin⁡(x))+8=−17x+12sin⁡(x)−8\left(- 17 x + 12 \sin{\left(x \right)}\right) + 8 = - 17 x + 12 \sin{\left(x \right)} - 8
- No
so, the function
not is
neither even, nor odd
    © Mister Exam – Calculator