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Question: sketch the function y 8 10x x2...

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Sketch the function y = 8 + 10x − x^2 over the domain [0,7]. (a) If xA = 1,xB = 4, and λ = 0.4. Using the formula x′ =λxA (1 − λ)xB, determine the value of x′. What is the value of f(x′)? (b) Calculate the value of y′, which is the value of the secant line at x′, using the formula y′ = λf(xA) (1 − λ)f(xB). (c) Prove that the above function is strictly concave by demonstrating that f(x′) > y′.

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