Find the coordinates that correspond to the maximum point of the following equation: y = −16x^2 + 160x - 256

To solve this problem, the maximum and minimum points of equations can be deduced through the differentiation process. This looks at the gradient of the function and the maximum/minimum value occurs when the gradient is zero.

The differentiation process is as follows:

f(x)=Axⁿ

df(x)/dx = nAx^(n-1)

The equation

y = −16x² + 160x - 256

becomes

dy/dx= -32x+160

after differentiation and set dy/dx=0

0=-32x+160

x=5

and the corresponding value for y is:

y=-16(5²)+160(5)-256= 144

And so the coordinate of the maximum point is:

(5,144)