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)

Derive the following: f(x)=(96/x^2)+kx

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The fifth term of an arithmetic sequence is equal to 6 and the sum of the first 12 terms is 45. Find the first term and the common difference.

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

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