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Deffense [45]
2 years ago
14

Consider a function of the form f(x) = 7x^2 + ax, where a is a real number. What is the difference quotient of f(x) for all nonz

ero values of h?
A. 7h + a

B. 14x + 7h

C. 7x + 7h + a

D. 14x + 7h + a
Mathematics
2 answers:
Tasya [4]2 years ago
8 0

Answer:

We select option D: 14 x + 7 h + a

Step-by-step explanation:

To find the difference quotient for h we do:

[f(x+h) - f(x) ] / h

that is:

[7 (x+h)^2 + a (x+h) - 7x^2 - a x] / h

[ 7 (x^2+ 2xh + h^2) - 7x^2 - a x] / h

[ 7 x^2 + 14 x h + 7 h^2 + ax + ah - 7 x^2 - a x] / h

cancel out terms:

[ 14 x h + 7 h^2 + ah] / h

14 x + 7 h + a

mihalych1998 [28]2 years ago
6 0

Answer:

c

Step-by-step explanation:

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Suppose Samantha is walking at a constant speed of 0.5 miles every 6 minutes from her house to a coffee shop located 1.3 miles a
Effectus [21]

Answer:

a) It takes Samantha 12 minutes to walk 1 mile

b) It takes Tina 6 minutes to bike 1 mile

c) k(t) = 0.083t

d) m(t) = 0.167t

e) Tina arrives befora Samantha

Step-by-step explanation:

a) How many minutes does it take Samantha to walk 1 mile?

This is a direct rule of three problem. So:

6 minutes - 0.5 miles

x minutes - 1 mile

x = 6/0.5 = 12 minutes

It takes Samantha 12 minutes to walk 1 mile

b) How many minutes does it take Tina to bike 1 mile?

Quite similar to a)

1.5 minutes - 0.25 miles

x minutes - 1 mile

x = 1.5/0.25 = 6 minutes

It takes Tina 6 minutes to bike 1 mile

c) Write a function k that determines the number of miles Samantha has walked in terms of the number of minutes.

We know that it takes 6 minutes for Samantha to walk 0.5miles. To build our function k, we need to know how many miles Samantha walks a minute.

So

6 minutes - 0.5 miles

1 - minutes - x miles

x = 0.5/6 = 0.083 miles

So the number of miles in function of t is

k(t) = 0.083t

d) Write a function m that determines the number of miles Tina has biked in terms of the number of minutes since she started biking

Same logic as c). So:

1.5 minutes - 0.25 miles

1 minute - x miles

x = 0.25/1.5

x = 0.167

So the number of miles in function of t is:

m(t) = 0.167t

e)

Samantha will arrive when k = 1.3, so:

0.083t = 1.3

t = 15.66 minutes

Tina will aririve when m = 2.5, so:

0.167t = 2.5

t = 14.9 minutes

Tina arrives befora Samantha

4 0
3 years ago
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