2) 3) The position of a function is given by s(t) = 4t 2 + 2t + 3, where s is me

Question

2)

3)

The position of a function is given by s(t) = 4t2 + 2t + 3, where s is measured in feet and t in seconds. Find the velocity of the object at time t = 2 seconds. Include units in your answer.

4)

5)

Find the equation of the line tangent to f(x) = 3x2 + 2x + 7 at the point (1, 12).

6)

Use 4 inscribed rectangles to estimate the area between the graph of f(x) = x2 + x and the x-axis between x = 3 to x = 5. Give your answer to 3 decimal places. Your work must show the set up and evaluation of the area.

7)

Let f(x)=x/(x-1).Use calculus to show that f is decreasing wherever it is defined.

Explanation / Answer

6)

?x=(5-3)/4
=1/2
(3,(7/2)) , ((7/2),4) , (4,(9/2)) , ((9/2),5)
A=145/4
=36.25

5)

f(x)=3x^2+2(x)+7
f'(x)=(d/dx(7+2x+3x^2))
f'(x)=(d/dx(7))+(2d/dx(x))+(3d/dx(x^2))
f'(x)=6(x)+2
=6(1)+2
f'(x)=8

s(t)=4t^2+2(t)+3
s'(t)=d/dt(4t^2+2(t)+3)
s'(t)=d/dt(3)+2(d/dt(t))+4(d/dt(t^2))
s'(t)=2+8t
V=2+8(2)
V=16

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