Zeroes:
We must solve
![x^4-45x^2+324=0](https://tex.z-dn.net/?f=x%5E4-45x%5E2%2B324%3D0)
To do so, we define the auxiliary variable
. The equation becomes
![t^2-45t+324=0](https://tex.z-dn.net/?f=t%5E2-45t%2B324%3D0)
The quadratic formula yields the solutions
![t=9,\quad t=36](https://tex.z-dn.net/?f=t%3D9%2C%5Cquad%20t%3D36)
Substituting back
gives
![x^2=9 \iff x=\pm 3,\quad x^2=36 \iff x=\pm 6](https://tex.z-dn.net/?f=x%5E2%3D9%20%5Ciff%20x%3D%5Cpm%203%2C%5Cquad%20x%5E2%3D36%20%5Ciff%20x%3D%5Cpm%206)
So, the zeroes are -6, -3, 3, 6.
Turning points:
Turning points are points where a function stops being increasing to become decreasing, or vice versa. Since functions are increasing when their first derivative is positive and decreasing when it's negative, turning points are points where the first derivative is zero.
We have
![f(x)=x^4-45x^2+324 \implies f'(x)=4x^3-90x](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E4-45x%5E2%2B324%20%5Cimplies%20f%27%28x%29%3D4x%5E3-90x)
If we set the derivative to be zero, we have
![4x^3-90x=0 \iff x(4x^2-90)=0](https://tex.z-dn.net/?f=4x%5E3-90x%3D0%20%5Ciff%20x%284x%5E2-90%29%3D0)
So, the derivative is zero if x=0 or
![4x^2=90 \iff 2x^2=45 \iff x^2=\dfrac{45}{2}\iff x=\pm\sqrt{\dfrac{45}{2}}](https://tex.z-dn.net/?f=4x%5E2%3D90%20%5Ciff%202x%5E2%3D45%20%5Ciff%20x%5E2%3D%5Cdfrac%7B45%7D%7B2%7D%5Ciff%20x%3D%5Cpm%5Csqrt%7B%5Cdfrac%7B45%7D%7B2%7D%7D)
Hewwo dere fello citizen, The answer is 274 1/2cm! Rate me five stars and meow! :3
Answer:
Children who are taught refusal skills are more likely to make positive choices and refrain from engaging in high-risk behaviors
Step-by-step explanation:
The scale drawing of the computer lab will have a length of 4 centimeter and a widtgh of 6 centimeter.
Answer:
15, 17, 19
Step-by-step explanation:
x + x+2 + x+4 = 15 + (x+2 + x+4)
3x + 6 = 15 + 2x + 21
x = 15
x+2 = 17
x+4 = 19