(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

step-by-step explanation:

sorry but i cant draw that