Suppose that the function h is defined, for all real numbers, as follows.=hx −14x2    ≤if x−2−+x12    <−if 2≤x2−3    >if x2Find h−2, h1, and h5.

Suppose that the function g is defined, for all real numbers, as follows.=gx 2    ≤if x−2−+x122    <−if 2<x2+−14x1    ≥if x2Find g−5, g−2, and g−1.

Consider the function f : IR3 → IR defined byf (x) = 12 (x1)2 + 12 (x2)2 + 12 (x3)2 + ln(1 + (3x1 − x2 + 7x3 − 2)2) + 1.1(5x2 + 2x3 − 1)2(a) (5 points) Let h : IR2 → IR be defined by h(y) = ln(1 + (y1)2) + 1.1(y2)2. Show that∥∇2h(y)∥2 ≤ 2.2 for all y ∈ IR2.(b) (20 points) Suppose that the steepest descent with constant stepsize α = 0.01466 is applied tominimize f . Argue that any accumulation point of the sequence generated is a stationary pointof f

Let f(x) = −x5 −2x4 + 12x3 +x−1. Then either show that there is an x such thatf(x) = 0, and find an interval where it exists; or, show there is no such x.

The function h is defined as follows.=hx−−5x27If the graph of h is translated vertically downward by 3 units, it becomes the graph of a function g.Find the expression for gx.Note that the ALEKS graphing calculator may be helpful in checking your answer.=gx

Question No 54.Let f(x) and h(x) be functions defined as f(x) = 2x + 4 and h(x) = 2(2x – 2) – 2(x + 2) + 16. Find the largest value of 'x' such that f(x) = 4h(x).