1. Tanner Hueglin hit a game-winning home run to help the Toronto Quadratics win last year's World Series. The path of the ball can be described by the function h(t) = -5t2 + 30t +0.8 where h represents the height of the ball in metres above the ground and t is the time in seconds after it was hit. a) At what height did Tanner make contact with the ball? [A1/] b) Find the maximum height of the ball above the ground. How long does it take for the ball to reach this maximum height? [A5/] c) After how many seconds does the ball hit the ground? *exact answer - radical and reduced* [A5-
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.
![1. Tanner Hueglin hit a game-winning home run to help the Toronto
Quadratics win last year's World Series. The path of the ball can be
described by the function h(t) = -5t2 + 30t + 0.8 where h
represents the height of the ball in metres above the
ground and tis the time in seconds after it was hit.
a) At what height did Tanner make contact with the ball?
[A1 ]
b) Find the maximum height of the ball above the ground. How long
does it take for the ball to reach this maximum height?
[A5 ]
c) After how many seconds does the ball hit the ground?
*exact answer - simplified radical and reduced*
[A5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc587742-696c-4790-93a1-f37a493780b9%2F0ee46b22-99e4-4352-81ee-10414a890753%2F3jmdgml_processed.jpeg&w=3840&q=75)
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