Plss help quick its easy

Let h(x) be a function whose second derivative is h 00(x) = x 3 − 4x 2 + 5x. h(x) has critical points at x = −1, x = 0, and x =

leva [86]

Answer:

*The function has a minimum in x=-1

*The function has a maximum in x=1

*The second derivative is not enough to determine if the function has either a maximum or a minimum in x=0.

Step-by-step explanation:

1. Evaluate the second derivative in the first critical point x=-1:

$h"(x)=x^{3}-4x^{2}+5x$

$h"(-1)=(-1)^{3}-4(-1^{2})+5(-1)$

$h"(-1)=-1-4-5$

$h"(-1)=-10$

As the value is smaller than zero, the function has a minimum in x=-1

2. Evaluate the second derivative in the second critical point x=1

$h"(x)=x^{3}-4x^{2}+5x$

$h"(1)=(1)^{3}-4(1^{2})+5(1)$

$h"(1)=1-4+5$

$h"(1)=2$

As the value is larger than zero, the function has a maximum in x=1

3. Evaluate the second derivative in the third critical point x=0

$h"(x)=x^{3}-4x^{2}+5x$

$h"(0)=(0)^{3}-4(0^{2})+5(0)$

$h"(0)=0-0+0$

$h"(0)=0$

As the value is equal to zero, the second derivative is not enough to determine if the function has either a maximum or a minimum in x=0.

6 0

3 years ago

The cost of an iPhone is $899.99 plus 8.5% tax. What is the cost of tax for the iPhone?

Sliva [168]

Answer:

724.0915

Step-by-step explanation:

multiply 899.99 and 8.5 you get 724.0915

hope this helps

7 0

2 years ago

What is the factored form of the function f(x)=x^3+8x^2+5x−50?

Inga [223]

Answer:

the factors of f(x)=x^3+8x^2+5x-50 are (x-2)(x+5)(x+5)

Step-by-step explanation:

We need to factorise the function $f(x)=x^3+8x^2+5x-50$

If a number is a factor of this function than it must be completely divisible by last co-efficient. Our last co-efficient is -50

Checking few numbers:

$f(1)=(1)^{3}+8(1)^2+5(1)-50\\f(1)=1+8+5-50\\f(1)=-32\\Now \ putting \ x= 2 \\f(2)=(2)^{3}+8(2)^2+5(2)-50\\f(2)=8+8(4)+10-50\\f(2)=8+32+10-50\\f(2)=0$

So, f(2)=0 which means x-2 is a factor of the given function. Now we will perform long division of $x^3+8x^2+5x-50$ by (x-2) to find other factors

The long division is shown in figure attached.

After long division we get: $x^2+10x+25$

The equation $x^2+10x+25$ can be further simplified as: (x+5)(x+5) or (x+5)^2

So, the factors of f(x)=x^3+8x^2+5x-50 are (x-2)(x+5)(x+5)

3 0

3 years ago

A plane flying horizontally at an altitude of 2 mi and a speed of 540 mi/h passes directly over a radar station. Find the rate a

Rasek [7]

Answer:

The plane's distance from the radar station will increase about 8 miles per minute when it is 5 miles away from it.

Step-by-step explanation:

When the plane passes over the radar station, the current distance is the altitude h = 2. Then it moves b horizontally so that the distance to the station is 5. We can form a rectangle triangle using b, h and the hypotenuse 5. Therefore, b should satisfy

h²+b² = 5², since h = 2, h² = 4, as a result

b² = 25-4 = 21, thus

b = √21.

Since it moved √21 mi, then the time passed is √21/540 = 0.008466 hours, which is 0.51 minutes. Note that in 1 minute, the plane makes 540/60 = 9 miles.

The distance between the plane and the radar station after x minutes from the moment that the plane passes over it is given by the function

$f(x) = \sqrt{((9x)^2 + 2^2)} = \sqrt{(81x^2+4)}$