(For this problem, you are welcome to use any computational tools that would be helpful.)

Let f(x)=13x3−x2−3x+10 defined on the interval [−4,4].

Let x1 and x2 be the critical points of f, and let's impose that x1
x1=

unanswered

x2=

unanswered

Fill in the next two boxes with the values of f′′(x1) and f′′(x2), respectively:

f′′(x1)=

unanswered

f′′(x2)=

unanswered

x1 = -0.2529 (Maximum point)

x2 = 0.3042 (Minimum point)

Step-by-step explanation:

Critical point of any polynomial may be by calculating f'(x) = 0. To further classify each critical point as minimum or maximum, we substitute the critical points in second derivative of the function. If the answer of f"(x) is positive, the respective critical point is minimum, if the value is negative then the critical point is maximum.

Step 1:  Differentiate the function f(x)

Step 2: f'(x) = 0

Step 3: Solving the quadratic equation using the formula:

These are the two critical points of the function.

Step 4: Calculating second derivative of the function

Step 5: Substituting values of x1 and x2 in f''(x)

As stated earlier, if the value of f''(x) is negative, the point is maximum and vice versa.

⇒ maximum point

⇒ minimum point

25

step-by-step explanation:

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.