A kid launches a bottle rocket off of a launch pad. The rocket's height above the ground (in feet) t seconds after its launch is given by the function, h(t) = -t^(2) + 16t + 4= -(t-8)^(2) +68= -(t-(8+2 \sqrt(17))) (t+(8+2\sqrt(17)) At what time does the rocket reach its maximum height? what is the height of the launch pad that the rocket was launched from?  How long does it take unitl the rocket land on the ground?

Q: A cat is falling from a branch. Its height t seconds after it fell is given by the function h(t) =…

A: We have given height  ht=-16t2+5 To get for what height cat was falling  Put t=0 h0=0+5 h0=5 height…

Q: g(x)=-1/5x^2-5x+7 What is the Leading Term of the Polynomial?

A: We know that the leading term is the term containing the highest power of the variable. Given…

Q: If an object is thrown directly from t seconds s (t) = -16t ^ 2 + 48t + 256 feet after t seconds.…

A: For maxima, [double derivative of  s(t)]<0.

Q: Given the function: f(x)=4x^2-9x, evaluate/simplify the following: f(x+h)-f(x)/h

A: Given function f(x)=4x2-9x To Evaluate f(x+h)-f(x)h

Q: p(t)=-1718^2+82000+10000

A: Given:p(t)=-17182+82000+10000

Q: 4) 36 cm/sec to mph

A: Please see the answer below

Q: f(x)=x^3-7x^2-x+7 How do I multiply the factors to put the function into polynomial form?

A: We have to factor in the given polynomial.…

Q: Given g(x)= 6x^2-x+9 a. g(0) b. g(-1) c g(r) d g(x+h)

A: To find the value of the given function at specified values.

Q: A young boy shoots a rocket off of a table and the height of the rocket in meters is given by h(t) =…

A: Here we have to find the time and height.

Q: Convert f(x)=(x-3)(X^2 -5x +6) into factored form

A:

Q: In the function:  f(x)= (9x^2)/ ((x^2)-49) Indicate the domain and range in interval notation.  What…

A: Denominator of the function can not be equal to 0.

Q: Given the functions f (a) = -a2 +3x +4 and g (x) = -5x- 6. find (go f) (2)=- (Use ^ for exponents,…

A:

Q: show that the difference quotient of f(x)=square root of x can be written as 1/the square root of…

A:

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.