Juan borrows $ 100 , 000 to pay for medical school. He borrows part of the money from the school whereby he will pay 4.5 % simple interest. He borrows the rest of the money through a government loan that will charge him 6 % interest. In both cases, he is not required to pay off the principal or interest during his 4 yr of medical school. However, at the end of 4 yr , he will owe a total of $ 19 , 200 for the interest from both loans. How much did he borrow from each source?
Juan borrows $ 100 , 000 to pay for medical school. He borrows part of the money from the school whereby he will pay 4.5 % simple interest. He borrows the rest of the money through a government loan that will charge him 6 % interest. In both cases, he is not required to pay off the principal or interest during his 4 yr of medical school. However, at the end of 4 yr , he will owe a total of $ 19 , 200 for the interest from both loans. How much did he borrow from each source?
Solution Summary: The author calculates the amount of money borrowed by Juan from the school and the government that will charge him 6% interest.
Juan borrows
$
100
,
000
to pay for medical school. He borrows part of the money from the school whereby he will pay
4.5
%
simple interest. He borrows the rest of the money through a government loan that will charge him
6
%
interest. In both cases, he is not required to pay off the principal or interest during his
4
yr
of medical school. However, at the end of
4
yr
, he will owe a total of
$
19
,
200
for the interest from both loans. How much did he borrow from each source?
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
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