Calculus Find the equation of a tangent line at a point and velocity
Find the equation of the line tangent to a curve at the given point.
1.
F(x) = x 2 +1 (2,5)
2.
F(x)= x-2x 2 (1, -1)
3.
F(x)= 8/x 2 (2,2)
4.
F(x) = 5x2 x=-1
5.
F(x)= 1- x 2 x= 2
6.
F(x)= x 2 -2 x=1
7.
F(x)= x 2 -3x at x=-2
8.
F(x)= x 2 -2 at x=0
9.
F(x)= 1/ (x-1) at x=3
10.
F(x)= 4-x 2 (-1,3)
11.
F(x)= (x-1) 2 +1 (1,1)
12.
F(x)=x 3 (-2,-8)
Rates of Change (velocity)
13.
An object is dropped from the top of a 100m high tower. Its height above ground after t seconds is 100-4.9m. How fast is it falling 2 sec after it is dropped? (use units)
14.
At t seconds after lift-off, the height of a rocket is 3t2 ft. How fast is the rocket climbing after 10 seconds? (use units)
15.
What is the rate of change of the area of a circle (A=r 2 ) with respect to its radius when the radius is r=3? (use units)
16.
What is the rate of change of the volume of a ball (V= 4/3 π r 3 ) with respect tot the radius when the radius is r=2? (Use units)
17.
A particle move according to a law of motion s= f(t), t> 0, where t is measured in seconds and s in feet. a.
What is the general equation for velocity? b.
What is the velocity after 3 seconds c.
When is the particle at rest? d.
When is the particle moving in the positive direction?

18.
If a ball is thrown vertically upward with a velocity of 80 ft/sec, then its height after t secons is s=80t-16t 2 . a.
What is the maximum height reached by the ball? b.
What is the velocity of the ball when it is 96 feet above the ground on its way up? On its way down?
19.
Supposed that the cost, in dollars, for a company to produce x pairs of a new line of jeans is
C(x) = 2000 +3x +.01x
2 +.0002x
3 a.
Find the marginal cost function (general equation of the slope) b.
Find the slope at x=100 and explain its meaning.