MathDB

5

Part of 1983 National High School Mathematics League

Problems(2)

Twice Function

Source: 1983 National High School Mathematics League, Exam One, Problem 5

2/21/2020
f(x)=ax2−cf(x)=ax^2-c. If−4≤f(1)≤−1,−z≤f(2)≤5-4\leq f(1)\leq -1,-z\leq f(2)\leq 5, then (A)7≤f(3)≤26(B)−4≤f(3)≤15(C)−1≤f(3)≤23(D)−283≤f(3)≤353\text{(A)}7\leq f(3)\leq26\qquad\text{(B)}-4\leq f(3)\leq15\qquad\text{(C)}-1\leq f(3)\leq23\qquad\text{(D)}-\frac{28}{3}\leq f(3)\leq\frac{35}{3}
function
Maximum Value of Trigonometric Functions

Source: 1983 National High School Mathematics League, Exam Two, Problem 5

2/22/2020
Function F(x)=∣cos⁡2x+2sin⁡xcos⁡x−sin⁡2x+Ax+B∣F(x)=|\cos^2x+2\sin x\cos x-\sin^2x+Ax+B|, where A,BA,B are two real numbers, x∈[0,32π]x\in[0,\frac{3}{2}\pi]. MM is the maximun value of F(x)F(x). Find the minumum value of MM.
function