2. A ball is thrown downward from the top of a 90-story building. The distance, d, in feet, the ball is above the ground after t seconds is given by the function d = f(t) =-16t2-80t + 800. Determine f(2) and explain what it means. %3D 7 8. 3. A woman's height in centimeters can be predicted from the length of her femur using the function h(x) = 2.47x + 54.10, where x is the length of the femur in centimeters. Calculate the approximate height of a woman whose femur is 45.5 cm. 9. 4. Alexia's height is approximately 1.83 m. Calculate the approximate length of his femur. (Refer to problem 3.) 10 5. A checkerboard contains 64 squares. If two pennies are placed on the first square, four pennies on the second square. eight pennies on the third square, and so on, the number of pennies on the nth square can be found by the function A(n) = 2". Find the number of pennies placed on the 30th square. 11
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.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
