Created on 2024-06-20Asked by Michael Wright (Solvelet student)
Find the maximum value of the function f(x)=−2x2+4x+1.
Solution
To find the maximum value of the function f(x)=−2x2+4x+1: 1. Find the derivative of f(x): f′(x)=−4x+4. 2. Set the derivative equal to zero to find critical points: −4x+4=0⟹x=1. 3. Determine the value of f(x) at x=1: f(1)=−2(1)2+4(1)+1=−2+4+1=3. Therefore, the maximum value of the function is 3. Solved on Solvelet with Basic AI Model
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DefinitionThe problem of optimization means maximizing or minimizing a function with specific constraints. These problems may be optionally constrained, or unconstrained, and are solved using a range of techniques from calculus and the field of linear algebra. Ex: To maximize profit P(x) = 50x − x^2 where x is the number of units produced.
