Chapter 12.2, Problem 2ES

Evaluate the next integral

1. For each of the following, find the critical numbers of f, the intervals on which f is increasing or decreasing, and the relative maximum and minimum values of f. (a) f(x) = x² - 2x²+3 (b) f(x) = (x+1)5-5x-2 (c) f(x) = x2 x-9 2. For each of the following, find the intervals on which f is concave upward or downward and the inflection points of f. (a) f(x) = x - 2x²+3 (b) g(x) = x³- x (c) f(x)=x-6x3 + x-8 3. Find the relative maximum and minimum values of the following functions by using the Second Derivative Test. (a) f(x)=1+3x² - 2x3 (b) g(x) = 2x3 + 3x² - 12x-4

Find the Soultion to the following dy differential equation using Fourier in transforms: = , хуо, ухо according to the terms: lim u(x,y) = 0 x18 lim 4x (x,y) = 0 x14 2 u (x, 0) = =\u(o,y) = -y لو

Can you solve question 3,4,5 and 6 for this question

water at a rate of 2 m³/min. of the water height in this tank? 16) A box with a square base and an open top must have a volume of 256 cubic inches. Find the dimensions of the box that will minimize the amount of material used (the surface area). 17) A farmer wishes to

#14 Sand pours from a chute and forms a conical pile whose height is always equal to its base diameter. The height o the pile increases at a rate of 5 feet/hour. Find the rate of change of the volume of the sand in the conical pile when the height of the pile is 4 feet.

(d)(65in(x)-5 cos(x) dx mins by 5x-2x² 3x+1 dx -dx 20 Evaluate each the following indefinite integrals

19 Evaluate each the following definite integrals: a) લ b) (+3) 6) (2-2)(+33) dx

#11 If a snowball melts so its surface area decreases at a rate of 1cm²/min, find the rate at which the diameter decreases when the diameter is 6 cm.