Find the extreme values of the function and where they occur. f(x)=x-4sqrt(x)

1 answer:

3 0

The extreme values of the function f(x) = x - 4sqrt(x) occur at the values of x for which f'(x) = 0

f'(x) = 1 - 2/sqrt(x) = 0
sqrt(x) - 2 = 0
sqrt(x) = 2
x = 4
To check for minimum or maximum,
f''(x) = 1/(sqrt(x))^3 = 1/(sqrt(4))^3 = 1/(2^3) = 1/8 => the point is a minimum.

Therefore, the minimum value = f(4) = 4 - 4sqrt(4) = 4 - 4(2) = 4 - 8 = -4 and occurs at x = 4.

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An equilateral triangle with side length 7 cm is shown in the diagram, work out the area of the triangle.

ElenaW [278]

If a triangle has sides of 7 cm and it is an equilateral you can draw a line right down the middle to form two congruent triangles.

These smaller triangles have a hypotenuse of 7cm and a base of 3.5 cm (7/2)

To work out the height, use Pythagoras’ theorem.

a^2 + b^2 = c^2 where c is the hypotenuse and a and b are the other two sides

7^2 - 3.5^2 = 36.75

Square root answer

= 6.06 cm

That’s the height of the triangle

Area of a triangle is base x height divided by 2

So 7 x 6.06 = 42.43…

/2

= 21.2 cm^2 to one d.p

Hope this helped!
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3 years ago

Find the scale factor that was used to change

avanturin [10]

Answer:

C. 1/5

Step-by-step explanation:

Original * scale factor = Scaled

25 * SF = 5

Divide each side by 25

25/25 * SF = 5/25

SF = 1/5

4 0

3 years ago

Read 2 more answers

A circle has a radius of 5 centimeters. What is the area?

schepotkina [342]

Answer:

$25\pi$

Step-by-step explanation:

The formula for the area of a circle is $A=\pi r^{2}$ , r is your radius, A is your area, and π is pi (3.1415...). You plug in your radius, or 5 into r, square it, 25, and multiply it by pi. You may be asked to use a certain number of digits of pi, and in that case you multiply for example 3.14 by 25, however $25\pi$ is the exact answer.