find the open intervals on which the function f(x)=cos^2(2x) is increasing in the interval (0,2pi)

find the open intervals on which the function f(x)=cos^2(2x) is increasing in the interval (0,2pi)

An isosceles triangle has equal sides of constant length 10 feet. The vertex angle (the angle opposite the third side, (the base) is increasing at a rate of 12radian per minute.Find the rate at which...

Use linear approximation, i.e. the tangent line, to approximate 2.73 as follow: Let f(x)=x3 . The equation of the tangent line to f(x) at x=3 can be written in the form y=mx+b where...

Suppose the Sunglasses Hut Company's profit is given by the equation P=-0.02q2+3q-32, where P is the total profit, in thousands of dollars, and q is the total number of sunglasses sold, in...

A piece of cardboard measuring 8 inches by 12 inches is formed into an open-top box by cutting squares with side length x from each corner and folding up the sides. Find...

Let f(x)=x^2 and g(x)=(x-74)^2+27. There is one line with positive slope that is tangent to both of the parabolas y=f(x) and y=g(x) simultaneously.

Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x → ∞ x + 2 36x2 +1

According to H(t), would the temperature of the soda ever be zero?

Calculus I, Derivative t>=0

Air is being pumped into a spherical weather balloon. At any time t, the volume of the balloon is V(t) and its radius is r(t). a.) What do the derivatives dV/dr and dV/dt represent...

A clown is standing on a cliff that is 528 ft tall. The clown hurls a tomato into the air with a velocity of 128ft/sec. How fast is the tomato traveling when it hits the ground below? I...

If f(p)=q means that, at a price of p dollars, a sandwich shop can sell q thousands sandwiches per week, then give the meaning of the equations f(4.5) = 1.2 and f'(4.5) = -0.1

this is an implicit differiation problem

A plane flies horizontally at an altitude of 5 km and passes directly over a telescope on the ground that is tracking the plane. When the angle of elevation (i.e. the angle of the telescope...

Let f(x)=x^2 and g(x)=(x-1)^2+7. There is one line with positive slope that is tangent to both of the parabolas y=f(x) and y=g(x) simultaneously. y=?

h(x)=xsquare root of x;a=16 d/dx=xsquare root of x=xsquare root of x(2+lnx/2square root of x) Evaluate the derivative at the given value of a. h'(a)=...

limx-->infinity (square root(9x2+x) - 3x)

rewrite and simplify

I'm confused on the steps of solving this problem. Any help would be greatly appreciated!

Find the parabola with equation y = ax2 + bx whose tangent line at (2, 0) has equation y = 4x − 8.