Q1) Find the equation of the line tangent to the graph of f at (1, 11 ), where f
ID: 2841833 • Letter: Q
Question
Q1) Find the equation of the line tangent to the graph of f at (1, 11), where f is given by
f(x) = 9x3 ? 4x2 + 6
(Let x be the independent variable and y be the dependent variable.)
---------------------------------------------------------------------------------
---------------------------------------------------------------------------------
Q3) What is the formula for V, the volume of a sphere of radius r?
V=
---------------------------------------------------------------------------------
Q4) The gravitational attraction, F, between the earth and a satellite of mass m at a distance r from the center of the earth is given by
---------------------------------------------------------------------------------
(b) Find the instantaneous velocity of the tomato at t = 1.8.
= sec OR sec/m OR m/sec OR m/sec^2 OR m
(c) What is the acceleration at t = 1.8?
= m/sec2
(d) How high does the tomato go?
= m
(e) How long is the tomato in the air?
= sec
Explanation / Answer
(1)
f(x) = 9x3 ? 4x2 + 6 at ( 1 ,11 )
slope = f ' = 27x^2 - 8x = 19
so equation is
y - 11 = 19 ( x - 1 )
=> y = 19x -19 + 11
=> y = 19x - 8
(2)
f(x) = 6x3+ 9x2? 35x + 22
f '(x) > = 1
=> 18x^2 + 18x - 35 > = 1
=> 18x^2 + 18x - 36 >= 0
=> (x-1)(x+2) > = 0
=> x belongs to ( - inf , -2 ] U ( 1 , inf )
or
x < = -2 and x > = 1
so option is
3
(3)
v = (4/3) pi r^3
dv / dr = (4/3) pi ( 3r^2 )
= 4 pi r^2
so it is surface area of sphere
(4)
F = GM m / r^2
dF/dr = -GMm / r^4 * 2r
= - 2 GMm / r^3
(5)
(a)
f(t) = ?4.9t2+ 25t + 4
avg velocity = f(1.8) - f(0) / 1.8 - 0
= 33.124-4 / 1.8
= 16.18 m/sec
(b)
f ' ( t ) = -9.8 t + 25
f ' ( 1.8 ) = 7.36 m/sec
(c)
accelaration = f " (t) = -9.8 m /sec^2
(d)
max height => f ' = 0
=> -9.8t + 25 = 0 =>t = 2.55
so max height is f ( 2.55) = 35.88 m
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.