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)
