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lesantik [10]
3 years ago
13

Find the values of m and b that make the following function differentiable.

Mathematics
1 answer:
dimaraw [331]3 years ago
4 0
Now, bearing in mind that, for a graph, to be "differentiable", means a "smooth transition", not an abrupt edge or a "cusp", the first subfunction of the piece-wise is just a quadratic, the second subfunction is a linear, well, so the linear needs to hit the quadratic "smoothly", not make an abrupt edge, for that, the linear must continue the quadratic from 2 onwards, since 2 is the range edge.

now, what is the piece-wise when x = 2? well, f(2) = x² or (2)² or 4

that means, the linear needs to hit it at that point, to make it so, let's make it the slope of the linear, the same as the quadratic's.

what's the quadratic's slope? well, simple enough

\bf \left. \cfrac{dy}{dx}=2x \right|_{x=2}\implies 4\impliedby \textit{this means }
\begin{array}{llll}
mx+b\\
\uparrow \\
4
\end{array}

so we have y = 4x + b

now, recall, for the quadratic, when x =2, y = 4, so for the linear, when x = 2, y = 4 as well, this means

\bf 4 = 4(2) + b\implies 4=8+b\implies 4-8=b\implies \boxed{-4=b}
\\\\\\
mx+b\implies 4x-4\\\\
-------------------------------\\\\
f(x)=
\begin{cases}
x^2&x\le 2\\
4x-4&x\ \textgreater \ 2
\end{cases}

check the picture below.

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Use linear regression to find a
Inessa [10]

A function that fits the following points (0,5), (2,-13) is y = 9x + 5

<h3>Equation of a line</h3>

The equation of a line in slope-intercept form is expressed as;

y =mx +b

where;

m is the slope

b is the intercept

Given the following coordinates (0,5), (2,-13)

Slope = -13-5/2-0
Slope = -18/-2

Slope = 9

Since the y-intercept is b = 5, hence the equation of the line will be y = 9x + 5

Learn more on linear regression here; brainly.com/question/25987747

#SPJ1

6 0
2 years ago
Find the difference of 1-3/8
Vilka [71]
1-3=-2 so -2/8 is -1/4 so negative one fourth
3 0
3 years ago
A coffee stand sells cups of coffee for $6 and cups of tea for $3. Tuesday a total of 75 cups were sold and the total money coll
Lorico [155]

Answer:

46 Teas and 29 Coffees

Step-by-step explanation:

46×3= 138

29×6= 174

174+138=312

4 0
3 years ago
What kinds of regular polygons can be used for regular tesselations
Ahat [919]
To tessellate a surface using a regular polygon, the interior angle must be a sub-multiple (i.e. factor) of 360 degrees to cover completely the surface.

For a regular three-sided polygon, the interior angle is (180-360/3)=60 &deg;
       Since 6*60=360, so a regular three-sided polygon (equilateral triangle)            tessellates.
For a regular four-sided polygon, the interior angle is (180-360/4)=90 &deg;
       Since 4*90=360, so a regular four-sided polygon (square) tessellates.
For a regular five-sided polygon, the interior angle is (180-360/5)=108 &deg;
       Since 360/108=3.33... (not an integer), so a regular five-sided polygon           (pentagon) does NOT tessellate.
For a regular six-sided polygon, the interior angle is (180-360/6)=120 &deg;
       Since 3*120=360, so a regular six-sided polygon (hexagon) tessellates.


5 0
3 years ago
Read 2 more answers
43 ones times 3 tens = how many tens
romanna [79]
Well 43 ones times 3 tens is basically 43 times 30 which is 1,290
then divide that by ten to get how many tens and you will get 129 tens
hope this helps
3 0
3 years ago
Read 2 more answers
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