An angler hooks a trout and reels in his line at 3 in. / s. Assume the tip of the fishing rod is 11 ft above the water and directly above the angler, and the fish is pulled horizontally directly toward the angler (see figure). Find the horizontal speed of the fish when it is 17 ft from the angler. Decreasing at 3 in./s 11 ft Let x be the horizontal distance from the angler to the fish and z be the length of the fishing line, where both x and z are measured in inches. Write an equation relatin x and z. *+ 132° = 2? Differentiate both sides of the equation with respect to t. (2x) = ( 2z When the fish is 17 ft from the angler, its horizontal speed is aboutO in. /s. (Round to two decimal places as needed.)
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
![An angler hooks a trout and reels in his line at 3 in. /s. Assume the tip of the fishing rod is 11 ft above the water and directly
above the angler, and the fish is pulled horizontally directly toward the angler (see figure). Find the horizontal speed of the fish
when it is 17 ft from the angler.
Decreasing
at 3 in./s
11 ft
Let x be the horizontal distance from the angler to the fish and z be the length of the fishing line, where both x and z are measured in inches. Write an equation relating
x and z.
x + 1322 = z?
Differentiate both sides of the equation with respect to t.
dx
dz
(2x)= (2]
When the fish is 17 ft from the angler, its horizontal speed is about
in. /s.
(Round to two decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0bb861a-a74a-4663-bbeb-0fca4422e7c0%2F65d57a19-d6ba-4847-861e-7d722864d860%2F4k96gqg_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 4 images
