Calculus Answers

The graph of(x²+y²)²=4(x²-y²) shown in the figure is called lemnicate find the points on the graph that correspond to x=1 find the equation of the tangent line to the graph at each point found in point a find the points on the graph at which the tangent is horizontal

Let it be f (x) = 2x³ - 9x² - 10.

a) specify the zeros of the f derivate of the function.

b) with what variable x values does f on grow?

c) determine between the maximum and the minimum value of the function f and [-4, 4].

6. Ship A is travelling south at the rate of 2 km/hr, at the instant that ship B, which is 32

miles south of ship A, is travelling east at rate of 4 km/hr.

a) Are they separating or approaching at the end of 2 hrs, and at what rate?

b) At what time are they nearest together?

c) What is their minimum distance apart?

5. A spherical snowball with an outer layer of ice melts, so that the radius of the snowball

decreases at the rate of 1/5 cm/sec. Find the rate at which the volume decreases when the

diameter is 50 cm.

3. An open rectangular box w/ square ends to hold 6400 cu ft, is to be built at a cost of

Php 75.00 per sq ft. for the base and

Php 25.00 /sq ft for the sides. Find the most economical dimensions.

2. A boy is flying a kite at a height of 150 ft. If the kite moves horizontally away from the

boy at the rate of 20 ft/sec, how fast is the string being paid out when the kite is 250 ft from him?

Find the area between y=x^2 and x+y-2=0

A wall "h" meters high is 2m away from the building. The shortest ladder that can reach the building with one end resting on the ground outside the wall is 6m. How high is the wall in meters?

Minimum distance. Find the minimum distance from a point on the

positive x-axis (a, 0) to the parabola y^2 = 8x.

Let F(x)=∫

t−3

t

2+7

for − ∞ < x < ∞

x

(a) Find the value of x where F attains its minimum value.

(b) Find intervals over which F is only increasing or only decreasing.

(c) Find open intervals over which F is only concave up or only concave down.