5. Which value of x, with −4 ≤ x ≤ 4, corresponds to the global (absolute)...

Which value of x, with −4 ≤ x ≤ 4, corresponds to the global (absolute) maximum of the functions f(x) = x 2 (3x 2 − 4x − 36) + c, where c is some given real number?

(a) −2 (b) 2 (c) 3 (d) 0 (e) None of the above.

14. Find f(x) by solving the initial value problem. f 0 (x) = e x − 2x; f (0) = 2

(a) f (x) = e x − x 2 (b) f (x) = e x − x 2 + 1 (c) f (x) = e x − x 2 + 2 (d) f (x) = e x − x 2 + C (e) None of the above.

18. Let f(x, y) = 1 + x + y + x 2 + axy + y 2 be a function of two variables. Suppose it is always true that ∂f /∂x = ∂f /∂y . What is the value of a?

(a) Any value of a is possible since mixed partial derivatives are equal. (b) 0 (c) 2 (d) 1 (e) There is no such value of a since the partial derivatives must be different.

Please provide the correct solution for each problem for a thumbs up. thank you!

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Expert Solution

milcah answered 1 year ago

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