Let h(t) = -16t2nd power + 64t + 80 represent the height of an object above the ground after t seconds. determine the number of seconds it takes to achieve its maximum height. justify your answer. state the time interval, in seconds, during which the height of the object decreases. explain your reasoning.

Given equation is

We have to find the time interval by which height is maximum.

We start with differentiating .

Differentiating h(t) ,

Differentiating again

Since on double differentiating , we are getting a negative number, so the height is maximum.

And to find the time of maximum height, we set h'(t) to 0, that is

In second part, the height is decreasing means slope, h'(t) is less than 0. That is,

So the required time interval is

hello,

as we don't know if g(x) is continue,

answer b

f(x)=2x²-8x+1=2(x²-4x+4)+1-8=2(x-2)²-7

vertex is (2,-7) ( a minimum since coefficient of x² is > 0)

point m is on plane r