Derivatives and Differentiation of Functions: Rate Change in Radius of a Sphere

A spherical baloon is being inflated at a rate of 400 cubic cm/min. At what rate is the radius changing when the radius is 25 cm. GIVEN (V=4/3*pi*r^3)

Derivatives and differentiation: Rate of Change - Surface Area of a Cube

At what rate is the surface area of a cube changing the edge measures 5 inches and is changing at a rate of 2 in/min. GIVEN (A=6*s^2)

Function : Horizontal Tangent Line

Find the points at which the function has a horizontal tangent line. f(x)=x^2+4x+5

Functions: Equation of Tangent Line

Find the equation of the line tangent to the graph of f(x)=x^3+x at the point (-1,-2).

word problem derivatives

A ball is dropped from the top of a building which is 1000 feet tall. GIVEN (s(t)=-16t^2+v(initial)t+s(initial)) A. Write the position and velocity functions for the ball. B. Find the instantaneous velocity went t = 2 seconds. C. How long does it take the ball to reach the ground. Please solve using calculus (derivativ ...continues

Implicit Differentiation

Find dy/dx implicitly: x^2+6xy-5y+y^3=12

Proof that the derivative of the inverse cosine of x = -1/ sqrt(1-x^2)

The inverse cosine function has domain [-1,1] and range [0, pi]. Prove that (cos^-1)'(x) = -1 / sqrt(1-x^2)

Critical points of a polynomial of degree 3.

Give examples of polynomials of degree 3 that have no critical point, only one critical point, and two critical points.

Double Integral : Integrating with respect to two variables.

Please see the attached file for the fully formatted problem.

Mass and centroid of a Plane Lamina

Please see the attached file for the fully formatted problem. Find the mass and centroid of a plane lamina with the given shape and density delta, the region bounded by y = x2 and x = y2 delta(x,y) = x2 + y2.