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Mathematics

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3. What is the range of the quadratic function shown on the graph below?<br> ده ستA:

myrzilka [38]

Because of the symmetry of the parabola, its stationary point will always be in the middle of its x-intercepts (or zeroes). ...

4 0

3 years ago

Use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3).

Soloha48 [4]

Step 1: evaluate f(x+h) and f(x)

We have

$f(x+h) = -(x+h)^2+6(x+h)-5 = -(x^2+2xh+h^2)+6x+6h-5$

$= -x^2-2xh-h^2+6x+6h-5$

And, of course,

$f(x)=-x^2+6x-5$

Step 2: evaluate f(x+h)-f(x)

$f(x+h)-f(x)=-x^2-2xh-h^2+6x+6h-5-(-x^2+6x-5)=-2xh-h^2+6h$

Step 3: evaluate (f(x+h)-f(x))/h

$\dfrac{f(x+h)-f(x)}{h}=-2x-h+6$

Step 4: evaluate the limit of step 3 as h->0

$f'(x) = \displaystyle \lim_{h\to 0} \dfrac{f(x+h)-f(x)}{h}=-2x+6$

So, we have

$f'(1) = -2\cdot 1+6 = 4,\quad f'(2) = -2\cdot 2+6 = 2,\quad f'(3) = -2\cdot 3+6 = 0$

5 0

3 years ago

Hat is the metric system prefix for the quantity 0.000 001?

mezya [45]

In the metric system, you give a name to the following multiples: 10, 100, 1000, 0.1, 0.01, 0.001, and then you skip three places. So, you have

$\left.\begin{array}{cc}\vdots&\vdots\\1000000&\text{mega}\\1000&\text{kilo}\\100&\text{hecto}\\10&\text{deca}\\0.1&\text{deci}\\0.01&\text{centi}\\0.001&\text{milli}\\0.000001&\text{micro}\\\vdots&\vdots\\\end{array}\right.$