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- find the maximum and minimum values of the func- tion on the given interval y=2x2−4x+2, [0,3]Given ƒ(x) = ax2 + 2bx + c with a >0. By considering the minimum, prove that ƒ(x)>= 0 for all real x if and only if b2 - ac<=0.True or false? If k > 0, then all solutions of y' = −k(y − b) approach the same limit as t →∞.
- show the equation z^2-4ln(5z+2) = 0 has atleast one root in the interval ( 0,4)Use the intermediate value theorem to show 2x^3+5x^2-3x-5=1 has a solution on the interval (0,2)Apply Newton’s method to estimate the solution of x3 − x − 1 = 0 by taking x1 = 1 and finding the least n such that xn and xn+1 agree to three digits after the decimal point.
- Use the Intermediate Value Theorem to show there is a solution to x2 − 16 = 2 in the x2 − 9interval (1, 2).4. If the secant method is used on f(x) = x^5 +x^3 +3 and if x_(n-2) = 0 and x_(n-1) = 1, what is x_n?2. Give an example showing that, even if f0(c) = 0, it could happen that f(x) does not have a localmaximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?
- Show that the diophantine equation x^4 - y^4 = z^2 has no solutions in nonzero integers using the method of infinite descentfind the absolute maxima and minima of the func-tions on the given domains. ƒ(x, y) = x2 + y2 on the closed triangular plate bounded by the lines x = 0, y = 0, y + 2x = 2 in the first quadrant.2. Considerf(x) = ax^3 + x + 1,where a is a real-valued parameter. Find all possible values of a such that on the interval[−1, 1], f has global maximum equal to 4/3 and global minimum equal to 2/3.