Ask question

Ask question

All categories

3 years ago

13

I want to make sure i got this right. PLS HELP ASAP I NEED IT CALC 1 one question

1 answer:

IrinaK [193]3 years ago

6 0

$\bf f(x)=
\begin{cases}
x^3&x\le 1\\
mx+b&x\ \textgreater \ 1
\end{cases}$

now, a function may well be continuous, but it may not be differentiable.

graph wise, differentiability means, a smooth curve, with no abrupt spikes or drops or cuts.

so for this piece-wise to be differentiable, the subfunctions must meet at junctions smoothly, with no abrupt changes, so mx + b, must blend in with x³ smoothly.

now, that can only occur if mx + b has the same slope as x³ at that point where they meet. The point where they meet is at x = 1, well, let's check what is the slope of x³ at x = 1.

$\bf \cfrac{d}{dx}[x^3]\implies \left. 3x^2\cfrac{}{}\right|_{x=1}\implies 3(1)^2\implies 3$

therefore "m" for mx+b, must be 3 then.

now, what's the value of x³ at x = 1? well is just (1)³, which is 1.

so for 3x + b, when x = 1, it must also equals 1 as well, that way it meets x³, thus

3x + b

3(1) + b = 1

b = -2

check the graph below.

You might be interested in

Do you agree with the statement that " cubic functions must have at least 1 x-intercept but not more than 3, whereas quadratic f

vladimir2022 [97]

Answer:

Yes, I agree

Step-by-step explanation:

For the cubic function

A cubic function is represented as:

$f(x)=ax^3+bx^2+cx+d$

A cubic function may have 1, 2 or 3 x intercepts. This is shown below

For 3 x intercepts

$y = x^3 - x$

Equate y to 0

$x^3 - x = 0$

Expand

$x(x^2 - 1) = 0$

Express $x^2 - 1$ as difference of two squares

$x(x - 1)(x +1 ) = 0$

<em>x = 0 or 1 or -1</em>

For 2 x intercepts

$y = x^3 - x$

$y =(x-5)^2)(x+7)$

Equate y to 0

$(x-5)^2(x+7) = 0$

Expand

$(x-5)(x-5)(x+7) = 0$

<em>x= 5 or x = -7</em>

For 1 x intercept

$y = x^3$

Equate y to 0

$x^3 = 0$

Take cube roots of both sides

$x = 0$

It has been shown above that a cubic function may have 1, 2 or 3.

So, I agree to the statement

For the quadratic function

A quadratic function will not have any x intercept when the function can not be factorized;

E.g.

$y = x^2 + x + 17$

<em>The above function has no x intercept.</em>

A quadratic function will have at least 1 x intercept when the function can be factorized;

E.g.

$y = x^2- 6x + 9$

Equate y to 0

$x^2- 6x + 9 = 0$

Expand

$x^2 - 3x - 3x + 9 = 0$

$(x - 3)(x-3) = 0$

$x = 3$

We've shown that a quadratic may have no x intercept, and it may also have x intercept(s)

Hence, I agree to both statement

3 0

2 years ago

Leanne jumped a distance of 3 feet 8 inches. Monica jumped a distance of 4 feet 6 inches. How many more inches did Monica jump t

mote1985 [20]

Answer:

10 more inches

Step-by-step explanation:

6 0

2 years ago

Simplify give ur answer in index form.

kherson [118]

$\frac{( {j}^{4} \: \times \: {j}^{8}) ^{3} }{( {j}^{9} \: \div \: {j}^{2}) ^{2} }$

First we calculate the product of the denominator.

$\frac{( {j}^{12}) ^{3} }{( {j}^{9} \: \div \: {j}^{2}) ^{2} }$

Then we calculate the quotient of the numerator.

$\frac{( {j}^{12}) ^{3} }{( {j}^{7}) ^{2} }$

We multiply the exponents of the expression.

$\frac{ {j}^{36} }{ {j}^{14} }$

We divide.

$\boxed{ \bold{ {j}^{22} }}$

<h3><em><u>MissSpanish</u></em></h3>

3 0

2 years ago

A local hardware business wishes to find out how many of the local residents would use a delivery service. They call every tenth

Free_Kalibri [48]

It is systematic because they are going every tenth person, in a random manner.

7 0

3 years ago

What do i multiply 5/6 by to get 10/12

Vladimir79 [104]

Answer:

2

Step-by-step explanation:

you get 2 because 5 times 2 equals 10 and 6 times 2 equal 12. so you get 10/12

7 0

3 years ago

Read 2 more answers