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The volume, V cm³, of a metallic cube of side length x cm, is increasing at the constant rate of 0.216 cm3 s^-1 .
(a) Determine the rate at which the side of the cube is increasing when the side length reaches 6 cm.
(b) Find the rate at which the surface area of the cube, A cm², is increasing when the side length reaches 6 cm.
Use the rules of differentiation to differentiate the following functions.
a. f(x)=2x²+6x
b.g(x)=7x⁴-3x²
c.y(x)=(4x)³- 18x²+6x
d.h(x)=(3x+4)²
e.h(x)=9x⅔+2/4√x
Determine whether if lim f(c) = f(c)
x + c
1. f(x) = x+2; c = -1
2. f(x) = x-2; c = 0
3. (at c = -1 )
f(x) = {x ² - 1 if x = < -1}
f(x) = { (x - 1) ² - 4 if x = ≥ - 1}
4. (at c = 1 )
f(x) = {x³ - 1 if x = < 1}
f(x) = { x² +4 if x = ≥ 1}
Find the minimum value and maximum value of f (x,y,z)= 8x^2 -2y subject to x^2 + y^2 =1
Find the maximum value and minimum value of f(x,y,z)=xyz subject to x+y+z=1 x≥0; y≥0; z≥0
Evaluate integral of c (xy^4) ds where c is right half of the circle x^2 + y^2 =16 traced out in a counter clockwise direction parameterized using x=4cost, y=4sint
Use the rules of differentiation to differentiate the following functions.
1.f(x)=2x³+6x
2.g(x)=7x⁴-3x²
3.y(x)=(4x)³-18x²+6x
4.h(x)=(3x+4)²
5.h(x)=9x⅔+2/4√x
Using the Chain Rule, find the 𝑑𝑦/𝑑𝑥 and express the final answer in term of x.
𝑦 = 2𝑢/𝑢²−1 , u=x²
The volume, V cm3, of a metallic cube of side length x cm, is increasing at the constant rate of 0.216 cm3 s– 1 .
(a) Determine the rate at which the side of the cube is increasing when the side length reaches 6 cm.
(b) Find the rate at which the surface area of the cube, A cm2, is increasing when the side length reaches 6 cm.
Consider the function, f x( ) = 2x3 −24x2 −7. Find the intervals of x where f(x) is increasing or decreasing.
