The degree of the polynomial function f(x) is 3. The roots of the equation f(x)=0 are −4 , 0, and 2. Which graph could be the gr
aph of f(x) ?
2 answers:
We know that the polynomial function is of degree 3, and that its roots are -4, 0, 2.
With this data we can write a generic equation for the function:
f (x) = bx (x + 4) (x-2)
Since the function is of degree 3 and cuts the axis at x = 0, then it has rotational symmetry with respect to the origin.
The graph of the function can be of two main forms, based on the value of the coefficient b.
If b is positive then the function grows from y = -infinite and cuts the x-axis for the first time in -4. Then it decreases, cuts at x = 0 and begins to grow again cutting the x-axis for the third time at x = 2. and continues to grow until y = infnit
If b is negative, then the function decreases from y = infinity and cuts the x-axis for the first time in -4. Then it grows, cuts at x = 0 and begins to decrease again by cutting the x-axis for the third time at x = 2, and continues to decrease until y = -infnit.
In the attached images the graphs of the function f (x) are shown assuming b = -1 and b = 1
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Answer:
The rate at which water is being pumped into the tank is 13,913.27 cubic centimetre per minute
Step-by-step explanation:
Given that, the height of the conical tank is 13 meters and diameter is 3 meters.
Radius = meters
......(1)
The volume of the cone is
Now putting
Differentiating with respect to t
Given that, the water level is rising at a rate of 17 cm per minute when the height 1 meter= 100 cm .i.e cm/min
Putting
≈7,113 cubic centimetre per minute
The volume of water increases 7,113 cubic centimetre per minute while 6,800 cubic centimetre per minute is leaking out.
It means the required rate at which water is being pumped into the tank is
=(7,113+6,800)cubic centimetre per minute
=13,913 cubic centimetre per minute