F(x)= x2 . What is f(x) + f(x) + f(x)? (f(x)) f(x) + 3 [3f(x)

Use the definition of the derviative to compute the derivative of f(x)= 1- 7x^2 at the specific point x=2.

GaryK [48]

Answer:

$f'(x) = -28 \ at \ x = 2$

Step-by-step explanation:

$f'(2) = \lim_{h \to 0}\frac{f(2+h)) -f(2)}{h} \\\\f(2+h) = 1 - 7(2+h)^2 = 1 - 7(4 +h^2 +4h) = 1 - 28 - 7h^2 - 28h = - 7h^2 -28h - 27\\\\f(2) = 1 - 7(2^2) = 1 - 28 = -27\\\\f(2+h) - f(2) = -7h^2 - 28h - 27 - (-27) = -7h^2 -28h -27 + 27 = -7h^2 -28h\\\\f'(2) = \lim_{h \to 0}\frac{-7h^2 - 28h}{h} \\\\$

$= \lim_{h \to 0} \frac{h(-7h -28)}{h}\\\\= \lim_{h \to 0} (-7h -28)}\\\\= -7 (0) - 28\\\\= -28$

4 0

3 years ago

Find an equation of the plane that passes through the point P0 = (6, 3, 2) and is parallel to the xy-plane. g

Nutka1998 [239]

The xy-plane has a normal vector of 〈0, 0, 1〉, and any plane parallel to it will have the same normal vector.

Then the equation of the plane through (6, 3, 2) that is parallel to the xy-plane has equation

〈x - 6, y - 3, z - 2〉 • 〈0, 0, 1〉 = 0

==> z - 2 = 0

==> z = 2

3 0

3 years ago

During the past 10 years, the amount of money, M (in billions of dollars), spent in North America by car dealerships advertising

rewona [7]

Answer: I believe the 23rd, but if its in 10 years I must be wrong

I graphed the equation, but replaced t with x

6 0

3 years ago

Lana makes eight dollars an hour Plus $12 an hour for every hour overtime. Overtime hours are any hours more than 40 hours for t

vagabundo [1.1K]

Answer:

W = $8X

Step-by-step explanation:

Lana makes $8 per hour

Extra $12 an hour for every hour overtime

Overtime are hours more than 40 hours per week

In this case, Lana worked for X hours with no overtime

If W is wages earned for working for X hours , the equation will be;

W= X * $8

W= $8X

5 0

3 years ago

What ordered pair is a solution for y-4=7(x-6)

777dan777 [17]

The ordered pair (6 , 4) is a solution for y - 4 = 7(x - 6)

Step-by-step explanation:

The point-slope form of a linear equation is:

$y-y_{1}=m(x-x_{1})$ , where

m is the slope of the line
$(x_{1},y_{1})$ is a point on the line

Any point on the line is a solution for the equation of the line

The solution of an equation is the values of x and y which make the left hand side is equal to the right hand side

∵ The equation is y - 4 = 7(x - 6)

- Compare the equation by the point-slope form above

∴ m = 7

∴ $x_{1}$ = 6 and $y_{1}$ = 4

- That means point (6 , 6) lies on the line

∴ Point (6 , 4) is a point on the line which represents the

given equation

∵ Any point on a line is a solution of the equation of that line

∴ (6 , 4) is a solution of the equation

The ordered pair (6 , 4) is a solution for y - 4 = 7(x - 6)

Learn more:

You can learn more about the linear equations in brainly.com/question/1284310

#LearnwithBrainly

8 0

3 years ago