Finding the Absolute Maximum and Minimum on the Given Interval Introduction,Examples with Step-by-Step Explanations

The problems about Finding the Absolute Maximum and Minimum on the Given Interval

Topic	Problem	Solution
None	A rectangular garden of area 300 square feet is t…	Let the length of the side that will be surrounded by a fence be denoted as $x$ , and the length o…
None	Find the absolute maximum and minimum values of t…	We can write the expression as $k (x, y) = - (x^{2} - 4 x + 4) - (y^{2} - 4 y + 4)$
None	Maximize $Q = x^{2} y$ , where $x + 2 y = 50$ .	We are given the function $Q = x^{2} y$ and the constraint $x + 2 y = 50$ .
None	Find the maximum profit and the number of units t…	Define the profit function, $P (x)$ , as the difference between the revenue function, $R (x)$ , and…
None	Find the absolute maximum and minimum values of t…	The function given is $f (x) = 1 - 2 x - 4 x^{2}$ and we are asked to find the absolute maximum and mini…
None	Find the absolute maximum and minimum values of t…	The function is $f (x) = x^{2} + \frac{160}{x}$ and we are looking for its absolute maximum and minimu…
None	Find the absolute maximum and minimum values of t…	First, we need to find the derivative of the function $f (x) = x^{2} + \frac{160}{x}$ . Using the pow…
None	A dorm at a college houses 1200 students. One day…	First, we need to find when the flu is spreading the fastest. This is when the rate of change of th…
None	A supply company manufactures copy machines. The …	The unit cost $C$ is given by the function $C (x) = 0.4 x^{2} - 96 x + 16, 541$ .
None	Homing pigeons avoid flying over water. Suppose a…	The pigeon's path can be divided into two parts: the flight over water from C to some point S on th…
None	A Norman window is a rectangle with a semicircle …	Let the radius of the semicircle be $r$ and the height of the rectangle be $h$ . The perimeter o…
None	Find the dimensions of the open rectangular box o…	Given a sheet of cardboard of dimensions 43 inches by 23 inches, we are to cut out congruent square…
None	A lifeguard needs to rope off a rectangular swimm…	Let $x$ be the length of a side of the rectangle perpendicular to the shoreline. The total length o…
None	Find the absolute extrema of the function, if the…	The function given is a quadratic function, which is a parabola. The coefficient of $x^{2}$ is posi…
None	Find the absolute maximum and minimum values of t…	Given the function $f (x) = \frac{2 x}{x^{2} + 16}$ over the interval $[- 9, 9]$ .
None	Find the absolute maximum and minimum values of t…	The function given is $f (x) = x^{2} - 8 x - 4$ and we are asked to find the absolute maximum value…
None	Find the absolute maximum and minimum values of t…	The function given is a quadratic function, and its graph is a parabola opening downwards since the…
None	Enhanced Homework Part 6 of 8 where $A_{0}$ is th…	The function given is $A (t) = \frac{A_{0}}{t^{2} + 1}$ , where $A_{0}$ is the initial amount of the …
None	A company produces two types of solar panels per …	First, we need to find the profit function. The profit, P(x, y), is given by the revenue, R(x, y), …
None	Find the absolute maximum and minimum values of t…	Define the function $g (x) = 2 \csc (x)$ , which is equivalent to $g (x) = 2 / \sin (x)$ .
None	Find the extremum of $f (x, y)$ subject to the giv…	Define the function and the constraint: $f (x, y) = 40 - x^{2} - y^{2}$ and \(g(x, y) = x + 6y - 3…
None	Find the maximum profit and the number of units t…	Given the revenue function, $R (x) = 50 x - 0.1 x^{2}$ , and the cost function, $C (x) = 5 x + 30$ , we …
None	Find the minimum value of the function $f(x)=x^{2…	The function $f (x) = x^{2} + 6 x + 12$ is a quadratic function. The graph of a quadratic function is a …
None	Find the maximum profit and the number of units t…	Given the revenue function, $R (x) = 7 x - 3 x^{2}$ , and the cost function, \(C(x) = x^{3} - 5x^{2} …
None	A ball is thrown vertically upward. After $t$ sec…	Given the height function $h (t) = 72 t - 16 t^{2}$ , we need to find the time at which the ball reache…
None	Find the minimum value of the average cost for th…	The cost function is given by $C (x) = x^{3} + 37 x + 128$ .
None	Find the absolute extrema if they exist, as well …	First, we need to find the derivative of the function $f (x) = \frac{6 x}{x^{2} + 6}$ .
None	Find the absolute maximum and minimum values of e…	Find the derivative of the function $f (x) = 3 x^{3} - 3 x^{2} - 3 x + 5$ .
None	Find the points on the ellipse $4 x^{2}+2 y^{2}=1…	We are given the function $f (x, y) = x y$ and the constraint $4 x^{2} + 2 y^{2} = 1$ . We want to find …
None	Suppose we seek to optimize the objective functio…	Suppose we seek to optimize the objective function $f (x, y)$ subject to a constraint of the form …
None	An employee's monthly productivity $M$ , in number…	An employee's monthly productivity $M$ , in number of units produced, is found to be a function of t…
None	Find the maximum and minimum values of the functi…	Define the function $g (θ) = 2 θ - 9 \sin (θ)$ .
None	Consider the function $f(x)=2-6 x^{2}, \quad-4 \l…	Consider the function $f (x) = 2 - 6 x^{2}$ , for $- 4 \leq x \leq 2$ .
None	10 (b) Use calculus to find the value of $x$ for …	Let the wire be bent into a rectangle with sides of length a and b. The perimeter of the rectangle …
None	7 Seja $f (x) = 3 x^{2} - 2 x + m$ . a) Determine o valor…	$f (x) = 3 x^{2} - 2 x + m$
None	30. You have 64 feet of fencing to enclose a rect…	Given 64 feet of fencing, let the length of the plot be L and the width be W. The equation for the …