Answer:
f'(x) > 0 on 
and f'(x)<0 on
Step-by-step explanation:
1) To find and interval where any given function is increasing, the first derivative of its function must be greater than zero:
To find its decreasing interval :
2) Then let's find the critical point of this function:
![f'(x)=\frac{\mathrm{d} }{\mathrm{d} x}[6-2^{2x}]=\frac{\mathrm{d} }{\mathrm{d}x}[6]-\frac{\mathrm{d}}{\mathrm{d}x}[2^{2x}]=0-[ln(2)*2^{2x}*\frac{\mathrm{d}}{\mathrm{d}x}[2x]=-ln(2)*2^{2x}*2=-ln2*2^{2x+1\Rightarrow }f'(x)=-ln(2)*2^{2x}*2\\-ln(2)*2^{2x+1}=-2x^{2x}(ln(x)+1)=0](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cfrac%7B%5Cmathrm%7Bd%7D%20%7D%7B%5Cmathrm%7Bd%7D%20x%7D%5B6-2%5E%7B2x%7D%5D%3D%5Cfrac%7B%5Cmathrm%7Bd%7D%20%7D%7B%5Cmathrm%7Bd%7Dx%7D%5B6%5D-%5Cfrac%7B%5Cmathrm%7Bd%7D%7D%7B%5Cmathrm%7Bd%7Dx%7D%5B2%5E%7B2x%7D%5D%3D0-%5Bln%282%29%2A2%5E%7B2x%7D%2A%5Cfrac%7B%5Cmathrm%7Bd%7D%7D%7B%5Cmathrm%7Bd%7Dx%7D%5B2x%5D%3D-ln%282%29%2A2%5E%7B2x%7D%2A2%3D-ln2%2A2%5E%7B2x%2B1%5CRightarrow%20%7Df%27%28x%29%3D-ln%282%29%2A2%5E%7B2x%7D%2A2%5C%5C-ln%282%29%2A2%5E%7B2x%2B1%7D%3D-2x%5E%7B2x%7D%28ln%28x%29%2B1%29%3D0)
2.2 Solving for x this equation, this will lead us to one critical point since x' is not defined for Real set, and x''
≈0.37 for e≈2.72
3) Finally, check it out the critical point, i.e. f'(x) >0 and below f'(x)<0.
Answer:
=−ax+x2−3a+3x
Step-by-step explanation:
The total amount of the resulting mixture can be calculated by adding up the volume of the given substances assuming that volume addition is applicable given the properties of the fluids used.
That is,
T = 6 quarts + 10 quarts = 16 quarts
The total volume of the resulting mixture is 16.
Then, we do the component (antifreeze) balance by adding up the resulting antifreeze from the substances to the total. We let x be the percentage of antifreeze in the final mixture.
6(0.52) + 10(0.32) = 16(x)
The value of x from the equation is 0.395.
Therefore, the answer to this item is 39.5%.
Answer:
C. 8 units right and 5 units down
Step-by-step explanation:
since it's only a translation, take one point as an example. lets say the bottom right point on trapezoid P is point A, and the translated point on P' is A'. the coordinates of A are (-3,2) while the coordinates of A' are (5,-3). (-3+x,2+y)=(5,-3). -3+x=5, x=8; 2+y=-3, y=-5
Answer:
8
Step-by-step explanation:
You do 240 divided by 30 to get 8
