Question

The nature of the function f (x) = 2x – x^2 ​

Answer 1

Step-by-step explanation:

2x-x²=0

x(2-x) =0

x=0,x=2

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Answer 2

Answer:

f(x) is an increasing function

Step-by-step explanation:

f(x) = 2x-x²

=> f(1) = 2(1)-1² = 2-1 = 1,

f(2) = 2(2) - 2² = 4-4 = 0

f(3) = 2(3) - 3² = 6-9 = -3

f(4) = 2(4) - 4² = 8-16 = -24

not that if x increases, then f(x) also increases

=> f(x) is an increasing function

Note: you can also use differentiation method to find the same result for more complex functions