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1 year ago

Use Descartes rule to determine the possible number of positive and negative solutions for the polynomial: f(x)=10x^4-21x^2+11

Mathematics

1 answer:

galina1969 [7]1 year ago

3 0

Answer:

x = 11/2

Step-by-step explanation:

just go by each step

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Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the derivative does not exist at

KIM [24]

Answer:

The derivative of the function does not exist.

Step-by-step explanation:

The alternative form of a derivative is given by:

$f'(c)= \lim_{x \to c} \dfrac{f(x)-f(c)}{x-c}$

Our function is defined as:

h(x)=|x+8|

i.e. h(x)= -(x+8) when x+8<0

and x+8 when x+8≥0

i.e. h(x)= -x-8 when x<-8

and x+8 when x≥-8

Hence now we find the derivative of the function at c=-8

i.e. we need to find the Left hand derivative (L.H.D.) and Right hand derivative (R.H.D) of the function.

The L.H.D at a point 'a' is calculated as:

$\lim_{x \to a^-} \dfrac{f(x)-f(a)}{x-a}\\\\=\lim_{h \to0} \dfrac{f(a-h)-f(a)}{a-h-a}= \lim_{h\to 0} \dfrac{f(a-h)-f(a)}{-h}$

Similarly R.H.D is given by:

$\lim_{x \to a^+} \dfrac{f(x)-f(a)}{x+a}\\\\=\lim_{h \to 0} \dfrac{f(a+h)-f(a)}{a+h-a}= \lim_{h\to 0} \dfrac{f(a+h)-f(a)}{h}$

Now for L.H.D we have to use the function h(x) =-x-8

and for R.H.D. we have to use the function h(x)=x+8

L.H.D.

we have a=-8

$\lim_{x \to (-8)^-} \dfrac{h(x)-h(-8)}{x-(-8)}\\\\= \lim_{h \to0} \dfrac{h(-8-h)-h(-8)}{-8-h-(-8)}= \lim_{h\to 0} \dfrac{h(-8-h)-h(-8)}{-h}$

= $\lim_{h \to 0} \dfrac{8+h-8-0}{-h}= \lim_{h \to 0}\dfrac{h}{-h}=-1$

similarly for R.H.D.

$\lim_{x \to (-8)^+} \dfrac{h(x)-h(-8)}{x-(-8)}\\\\=\lim_{h \to 0} \dfrac{h(-8+h)-h(-8)}{-8+h-(-8)}= \lim_{h\to 0} \dfrac{h(-8+h)-h(-8)}{h}$

$\lim_{h \to 0} \dfrac{-8+h+8-0}{h}=\lim_{h \to 0}\dfrac{h}{h}=1$

Now as L.H.D≠R.H.D.

Hence, the function is not differentiable.

4 0

2 years ago

In order for an airline to cancel a flight, there needs to be over 6 inches of snow on the ground. Suppose we want to do a test

Lunna [17]

Answer:

Step-by-step explanation:

From the given question.

We can write the null hypothesis & the alternative hypothesis as:

Null hypothesis:

$\mathbf{H_o: \mu \leq 6}$

Alternative hypothesis:

$\mathbf{H_{a}:\mu >6}$

From above, let's think about the type I error we could make and the type II error we could make.

Type I error:

The type I error at the null hypothesis showcases that the snow level is at 6 inches or below 6 inches, but we falsely concluded that the snow level is high above sea level.

Type II error:

Here, the snow level is literally above 6 inches, hence, we failed to conclude that the snow level is above 6 inches.

Thus, the consequences of the above analysis showcase that type II error has higher severe consequences because it may result in a situation that may endanger the passengers' safety.

5 0

2 years ago

42 = -7 ( Z - 3 ) Z =?

ipn [44]

Answer:

-3

Step-by-step explanation:

6 0

3 years ago

A miner has 8 diamonds. He has 48 workers. Explain how each worker can get a piece of the diamonds.

Dmitrij [34]

Answer:

The worker can get a piece of the diamonds using 48÷8 which it is 6.

Step-by-step explanation:

I hope that it is what you're looking for. I hope this helps

6 0

2 years ago

Is 40 inch or 100 cm bigger

oksian1 [2.3K]

Answer:

40 inch

Step-by-step explanation:

1 inch=2.54cm

so 40 inch= 101.6 cm

7 0

3 years ago

Read 2 more answers

Use Descartes rule to determine the possible number of positive and negative solutions for the polynomial: f(x)=10x^4-21x^2+11​

Use Descartes rule to determine the possible number of positive and negative solutions for the polynomial: f(x)=10x^4-21x^2+11