Calculus Answers

The radius r (cm) of a circle at time t seconds is given by r = 9t - t^3 . At each of the following instants, find the rate of change of the radius (w.r.t.t) and state whether the radius is increasing or decreasing at these instants.
a) t =1 b) t =2 c) t =2.5

The maximum value of [x(x-1) +1]1/3 , 0 ≤ x ≤ 1 is ?

Using the product rule derivative how do you solve (4x+1)^2

f(x,y)=x^2y^3+x^4y, find:

1) ∂^2f/∂x^2
2) ∂^2f/∂y^2
3) ∂^2f/∂x∂y
4) ∂^2f/∂y∂x

a)solve the differential equation
y''-9y'+14y=e^4x

b)determine the order and degree of this equation

sketch the graph of 4x^2+9y^2-3z^2=36 and identify the surface

sketch the graph of the function f(x)=sinx

if f(x,y)=1/3x^3+4xy-9x- y''^2
a)find the local extreme and saddle point of f(x,y)
b)evaluate ∫ from 0 to 1 * ∫ from x^2 to 2x (x^3+4y) dy dx

sketch the garph of z=2x^2+2y^2 in 3 dimension

find the point of maximim and minimum for the function
z=f(x,y)=x^2-xy+y^2+3x-2y+1