Calculus Answers

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.

Find the coordinates of the points on the curve 𝑦 = 3𝑥3 − 2𝑥2 − 12𝑥 + 2 where the normal is parallel to the line 𝑦 = −𝑥 + 1.

The tangent to the curve 𝑦 = 2𝑥2 − 5𝑥 + 6 at the point (2,1) intersects the normal to the same curve at the point (1,4) at point 𝑄. Find the coordinates of 𝑄

Find the first and second derivative of the following:

1. y=cos x²

2.y=sinx cos x²

3.y=xsin x²

4.y=x cos x²