MHB Determining if a function is injective

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To determine if the function x³-5x²+3x+5 is injective, one must check for local extrema. A function is not injective if it has a local maximum or minimum, as it will take the same value at different points. Analyzing the derivative can reveal critical points where the function may change direction. If the derivative does not change sign, the function is injective. Thus, examining the behavior of the derivative is essential for establishing injectivity.
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is the function x³-5x²+3x+5 injective. how can you tell
 
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Re: calculus

You can determine if the function has a local extremum. If a function is continuous and has, say, a maximum, then it is not injective since it assumes the same values on both sides of that point of maximum.
 

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