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Salsk061 [2.6K]
3 years ago
13

Question 1(Multiple Choice Worth 2 points) Find the derivative of f(x) = 7 divided by x at x = 1.

Mathematics
2 answers:
nydimaria [60]3 years ago
5 0

Answer:

Step-by-step explanation:

Vaselesa [24]3 years ago
5 0

Question 1:

For this case we must find the derivative of the following function:

f (x) = \frac {7} {x} evaluated at x = 1

We have by definition:

\frac {d} {dx} [x ^ n] = nx ^ {n-1}

So:

\frac {df (x)} {dx} = - 1 * 7 * x ^ {- 1-1} = - 7x ^ {- 2} = - \frac {7} {x ^ 2}

We evaluate in x = 1

- \frac {7} {x ^ 2} = - \frac {7} {1 ^ 2} = - 7

ANswer:

Option A

Question 2:

For this we must find the derivative of the following function:

f (x) = 4x + 7\ evaluated\ at\ x = 5

We have by definition:

\frac {d} {dx} [x ^ n] = nx ^ {n-1}

The derivative of a constant is 0

So:

\frac {df (x)} {dx} = 1 * 4 * x ^ {1-1} + 0 = 4 * x ^ 0 = 4

Thus, the value of the derivative is 4.

Answer:

Option A

Question 3:

For this we must find the derivative of the following function:

f (x) = 12x ^ 2 + 8x\ evaluated\ at\ x = 9

We have by definition:

\frac {d} {dx} [x ^ n] = nx ^ {n-1}

So:

\frac {df (x)} {dx} = 2 * 12 * x ^ {2-1} + 1 * 8 * x ^ {1-1} = 24x + 8 * x ^ 0 = 24x + 8

We evaluate for x = 9we have:

24 (9) + 8 = 224

Answer:

Option D

Question 4:

For this we must find the derivative of the following function:

f (x) = - \frac {11} {x}\ evaluated\ at\ x = 9

We have by definition:

\frac {d} {dx} [x ^ n] = nx ^ {n-1}

So:

\frac {df (x)} {dx} = - (- 1 * 11 * x ^ {- 1-1}) = 11x ^ {- 2} = \frac {11} {x ^ 2}

We evaluate for x = 9 and we have:

\frac {11} {9 ^ 2} = \frac {11} {81}

ANswer:

Option D

Question 5:

For this case we have by definition, that the derivative of the position is the velocity. That is to say:

\frac {d (s (t))} {dt} = v (t)

Where:

s: It's the position

v: It's the velocity

t: It's time

We have the position is:

s (t) = 1-10t

We derive:

\frac {d (s (t))} {dt} = 0- (1 * 10 * t ^ {1-1}) = - 10 * t ^ 0 = -10

So, the instantaneous velocity is -10

Answer:

-10

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