MTH341
Question: A function \\(f: E \\rightarrow R\\) defined on a set \\(E \\subset R\\) is said to be _________ on E if \\( \\forall x_1, x_2 \\in (x_1 < x_2 \\Rightarrow f(x_1) \\geq f(x_2)\\)).
Answer: increasing
Question: A function \\(f: E \\rightarrow R\\) defined on a set \\(E \\subset R\\) is said to be _________ on E if \\( \\forall x_1, x_2 \\in (x_1 < x_2 \\Rightarrow f(x_1) \\geq f(x_2)\\)).
Answer: nonincreasimg
Question: A function \\(f: E \\rightarrow R\\) defined on a set \\(E \\subset R\\) is said to be _________ on E if \\( \\forall x_1, x_2 \\in (x_1 < x_2 \\Rightarrow f(x_1) > f(x_2)\\)).
Answer: decreasing
Question: What is the intervals in which the function f defined on R by f(x) = \\(2x^3 – 30x^2 +144x + 7 \\forall x \\in R\\) is decreasing?
Answer: [4, 6]
Question: Let \\(f: R \\rightarrow R\\) be defined as f(x) = x for \\(0 leq x < 1\\) and f(x) = 1 for \\(x \\geq 1\\). When is f(x) continuous?
Answer: x = 1
Question: A function \\(f: E \\rightarrow R\\) defined on a set \\(E \\subset R\\) is said to be _________ on E if \\( \\forall x_1, x_2 \\in (x_1 < x_2 \\Rightarrow f(x_1) < f(x_2)\\)).
Answer: increasing
Question: Let a function f be defined on an interval I. If f is derivable at a point \\(c \\in I\\), then it is ________ at c.
Answer: continuous
Question: Let \\(f : R \\rightarrow R\\) be a function defined as f(x) = \\(x^n \\forall x \\in R\\) where n is a fixed positive integer. What is the differentiability of f at any point \\( x \\in R.\\)?
Answer: f\'(x) = \\(nx^{n-1}\\)
Question: What is the intervals in which the function f defined on R by f(x) = \\(2x^3 – 30x^2 +144x + 7 \\forall x \\in R\\) is increasing?
Answer: \\(]-\\infty, 4] and [6, \\infty[\\)
