Vanessa throws a tennis ball into the air. The function h(t) below represents the distance, in inches, that the ball is from the ground at any time t, in seconds. h(t) = - 16t2 +64t+80 Graph the function in your calculator and use it to help you answer the questions below Do not include units in your answers, only numbers. What is the height of the ball when it is launched. At what time, will the ball reach the ground? What time will the ball reach its maximum height? What is the maximum height the ball will reach?

Q: Q4: Using Gauss-elimination method, determine the r,s,t for the system: * -21- 4s – 2t =-r 2t + 2r…

A: Given  -21-4s-2t=-r2t+2r+s-3=0-t+2+3r=-2s ⇒ -4s-2t+r=21s+2t+2r=32s-t+3r=-2 Rewrite the system in…

Q: Graph the function h (x)=-3x-2. 8

A:

Q: A ball thrown upwards is represented by the function h(t) = = 16t² + 50t +6 (height in feet, + in…

A:

Q: The cost of producing xgallons of Slurm is given by the function ?(?) = 2? + 48. A gallon of Slurm…

A:

Q: x² + 10 f(x) = %3D x3 - 8 graph of the function.

A: To identify four ordered pairs on the graph of the function.fx=x2+10x3-8

Q: Mia jumps off a cliff into the ocean in Acapulco while on vacation.  Her height, h, above the water…

A:

Q: 3. Explain how you would graph f(x) = -2(34x-20)-6. Include the graph as part of your solution.

A: To plot a graph use the calculus rules: 1. f'(x)>0 (<0) implies f(x) is increasing…

Q: х + 40, where 4 b. The temperature (in degrees Fahrenheit) can be approximated by the function c(x)…

A: For a function, y=f(x) , x is the independent variable and y is the dependent variable . Consider…

Q: Pamela is selling cookies. She chargers 75 cents for each cookie with the ingredient costing 2.00…

A: Consider the given information:

Q: For Exercise, graph the function. -3 п(х) 2x + 7

A:

Q: Graph the function f (x) = = × - 7.

A: We can graph the function as below.

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.