Calculus Answers

Suppose that we know f(x) is a polynomial with critical points x=-1, x=2 and x=6. If we also that the 2nd derivative is f''(x) = -3x² +14x -4. If possible, classify each of the critical points as relative minimums, relative maximums. If it is not possible to classify the critical points clearly explain why they cannot be classified.

study the function : x^2/x-1

find the area of the surface that is generated by revolving to portion of the curve y=x^3 between x=0 and x=1 about x axis?

Find the volume of an object enclosed by cylinders z = y² +2, z = 4−y² and planes x = −1 and x = 2.

Differentiate the following without solving for y in terms of x.

1. x²/9 + y²/4 =1
2. x²/4 + y²=1
3. x²+ y²/9 =1

Differentiate the following without solving for y in terms of x.

1. x²+10x+y²+17=0
2. x²+y²-2x+4y=3
3. x² +y²+2y=45
4. x²-4x+y²+2y=15
5. x²-2x+y²+2y=23

Differentiate the following functions

1. y=(x²+5x+2)³
2. y=(2x²-x+3)⁵
3. y=(x²-2x+6)⁷
4. ∛4x-5
5. ∛6-7x

find the surface area of the object obtained by rotating y=4+3x^2, 1<=x<=2 about the y axis

Find the center of the mass of the four particles having the masses of 2, 3, 3 and 4 kg and located at the points (-1, -2), (1, 3), (0, 5), and (2, 1), respectively.

derivative y = arctan⁴(3x⁵)