Find f(x) using first principles where f(x)=(x^3+1)/X^2
Find f(x) using first principles where f(x)=(x^3+1)/X^2 fferentiate from first principles the function f(x) = +1...
QUESTION 1 [4] Differentiate the following function using first principles: f(x)=*+1 QUESTION 2 [6] Differentiate the following: 2.1 y = e-1 [1] 2.2 y = xê [1] 2.3 y = tx (1) 2.4 y = 2e* (1) 2.5 y = 2x2 – 3x3 [2]
QUESTION 2 (a) By the first principles of differentiation, find the following: (i) Derivative of F(x)= F'(-3) 1-X 2 + x (ii)
Given the function: f(x)=(x^2-4x+6)/(x-1)^2 a) Find the asymptotes of f, if any b) Find the first and the second derivatives of f c) Find the intervals of increase and decrease of f d) Find the relative maxima and the relative minima, if any e) Find the intervals where f is concave up and down, respectively, together with the points of inflection, if any.
(x + 1)2 Consider the function f(x) -. The first and second derivatives of f(x) are 1 + x2 2(1 – x2) 4x(x2 - 3) f'(x) = and f" (2) Using this information, (1 + x2) (1 + x2)3 (a) Find all relative extrema. (4 points) Minimum: Maximum: (b) Find the intervals of concavity for f(x) and identify any inflection points for yourself. (5 points) Concave up: Concave down: (c) Using the fact that lim f(x) = 1, and our...
1. Using the graph, find the following: a. f(-3) b. (f.(2) c. x where f(x) = 3 2. What is the domain of f(x) = V2x - 7? 3. If h(x) (4x-3)2 write f(x) and g(x) so that h(x) = (fºg)(x) 5
Find CDF for random variable X where f(x)= x from 0<x<1 and f(x)= 2-x from 1<x<2. (SAME function)
F. dr Find a function of such that of 8 and then evaluate where F(x, y) = < 3 + 2kg", 2y) and C is any smooth curve from (-2, 1) to (1,2).
Find moment generating function of geometric distribution f(x)=p*q^(x-1), where x=1, 2, ... and use it to find EX and DX (i.e. find the first and the second moments).
2. Let g(x) In f(x) where f(x) is a twice differentiable positive function on (0, o) such that f(x + 1) = x f(x) Then for N 1, 2, 3 find g" N+ 2 2. Let g(x) In f(x) where f(x) is a twice differentiable positive function on (0, o) such that f(x + 1) = x f(x) Then for N 1, 2, 3 find g" N+ 2
Consumer's surplus: A consumer has the utility function U(x,y) =e^((ln(X)+Y)^1/3) where X is the good in concern and Y is the money that can be spent on all other goods. (So the price of Y is normalized to be 1). The income of this consumer is 100. (a) (10pts) Derive the demand function of x for this consumer. Make sure that at every price of x, the consumer always has enough income to buy the amount of x as indicated...