Of all rectangles with a perimeter of 7, which one has the maximum area? (give the dimensions.)
1 answer:
You might be interested in
Answer:
a) , b)
.
Step-by-step explanation:
a) The graphic is enclosed to the problem. By visual inspection, an absolute maximum is found.
b) The exact method consists in the application of the First and Second Derivative Tests. First and second derivatives are, respectively:
The First Derivative Test consists in equalizing the first derivative to zero and solving the expression:
According to the second derivative, the critical point leads to a maximum. The remaining component is determined by evaluation the polynomial:
The exact solution is , indicating that graphic solution leads to a good approximation.
Answer:
- No real roots
Step-by-step explanation:
Given equation:
- x² + 2x + 3 = 0
On comparing the equation by ax² + bx + x = 0, We get: a = 1, b = 2 and c = 3
To Find the nature of the roots of the equation firstly we need to find the discriminant of the equation. The expression b²- 4ac is called the discriminant.
- Two Distinct real roots, if b² - 4ac > 0
- Two equal real roots, if b² - 4ac = 0
- No real roots, if b² - 4ac < 0
The discriminant is smaller than 0.
- <u>Hence, Equation has no </u><u>real</u><u> roots (no solution)</u>