Question 1

Find an equation of the tangent line to the parabola  at the point  .

Accepted Answer

The equation for the parabola can be written as $y=x^2+3x+2$. To find the slope of the tangent line at $(a,b)$, we take the derivative of the equation of the parabola and evaluate it at $x=a$:
$$f'(x) = 2x+3 \quad \implies \quad m = f'(a) = 2a+3.$$
We know that the point of tangency is $(a,b)=(\frac{5}{2},\frac{33}{4})$, so we have $a=\frac{5}{2}$ and $b=\frac{33}{4}$, and hence $m=2a+3=8$.

The equation of the tangent line passing through $(\frac{5}{2},\frac{33}{4})$ with slope $m=8$ can be written in point-slope form as:
$$y-\frac{33}{4} = 8(x-\frac{5}{2})$$
Simplifying gives:
$$y=8x-11$$

Therefore, the answer is B) 11eaae29_f544_5697_87fe_fbe3497b35fb_TB2067_11.

Question 2

Find the slope of the tangent line to the curve  at the point (-4 , 22)

Accepted Answer

The answer of Find the slope of the tangent line...

Question 3

Find the derivative of the function.

Accepted Answer

The answer of Find the derivative of the function. ...

Question 4

The cost (in dollars)of producing x units of a certain commodity is  Find the average rate of change with respect to x when the production level is changed from

Accepted Answer

The answer of The cost (in dollars)of producing x units...

Question 5

If  ,find  .

Accepted Answer

The answer of If  ,find  .
...

Question 6

If a cylindrical tank holds 10000 gallons of water,which can be drained from the bottom of the tank in an hour,then Torricelli's Law gives the volume of water remaining in the tank after t minutes as  Find the rate at which the water is flowing out of the tank (the instantaneous rate of change of V with respect to t)as a function of t.

Accepted Answer

The answer of If a cylindrical tank holds 10000 gallons...

Question 7

Find an equation of the tangent line to the curve  at the point (2 , 6)

Accepted Answer

The answer of Find an equation of the tangent line...

Question 8

The cost (in dollars)of producing x units of a certain commodity is  Find the instantaneous rate of change with respect to x when  (This is called the marginal cost.)

Accepted Answer

The answer of The cost (in dollars)of producing x units...

Question 9

If an equation of the tangent line to the curve  at the point where

Accepted Answer

To find the equation of the tangent line, we need to find the derivative of the function at the given point. 
f(x) = ln(x^4 + 16), so 
f'(x) = 4x^3 / (x^4 + 16)
At the point (1, ln(17)), we have x = 1, so 
f'(1) = 4 / 17. 
Using the point-slope form of the equation of a line, we can find the equation of the tangent line: 
y - ln(17) = (4/17) (x - 1)
y = (4/17) x - (4/17) + ln(17)
Simplify: 
y = (4/17) x + (13/17) - (4/17)
y = (4/17) x + 9/17
The corresponding answer choice is D.

Question 10

Use the definition of the derivative to find

Accepted Answer

The answer of Use the definition of the derivative to...

Quiz 2: Derivatives

Find an equation of the tangent line to the parabola at the point .

Find the slope of the tangent line to the curve at the point (-4 , 22)

Find the derivative of the function.

The cost (in dollars)of producing x units of a certain commodity is Find the average rate of change with respect to x when the production level is changed from

If ,find .

Find an equation of the tangent line to the curve at the point (2 , 6)

The cost (in dollars) of producing x units of a certain commodity is Find the instantaneous rate of change with respect to x when (This is called the marginal cost.)

If an equation of the tangent line to the curve at the point where

Use the definition of the derivative to find