All categories

3 years ago

How do you do these two questions?

Mathematics

1 answer:

Mice21 [21]3 years ago

4 0

Answer:

a) d²y/dx² = ½ x + y − ½

b) Relative minimum

Step-by-step explanation:

a) Take the derivative with respect to x.

dy/dx = ½ x + y − 1

d²y/dx² = ½ + dy/dx

d²y/dx² = ½ + (½ x + y − 1)

d²y/dx² = ½ x + y − ½

b) At (0, 1), the first and second derivatives are:

dy/dx = ½ (0) + (1) − 1

dy/dx = 0

d²y/dx² = ½ (0) + (1) − ½

d²y/dx² = ½

The first derivative is 0, and the second derivative is positive (concave up). Therefore, the point is a relative minimum.

You might be interested in

How can you use a number to explain what an integer and rational numberes are?

enot [183]

Natural numbers are all numbers 1, 2, 3, 4… They are the numbers you usually count and they will continue on into infinity.

Whole numbers are all natural numbers including 0 e.g. 0, 1, 2, 3, 4…

Integers include all whole numbers and their negative counterpart e.g. …-4, -3, -2, -1, 0,1, 2, 3, 4,…

All integers belong to the rational numbers. A rational number is a number

ab,b≠0

Where a and b are both integers.

Example

The number 4 is an integer as well as a rational number. As it can be written without a decimal component it belongs to the integers. It is a rational number because it can be written as:

or even

−8−2

Whereas

15=0.2

is a rational number but not an integer.

A rational number written in a decimal form can either be terminating as in:

15=0.2

Or repeating as in

56=0.83333...

All rational numbers belong to the real numbers.

If you look at a numeral line

picture05

You notice that all integers, as well as all rational numbers, are at a specific distance from 0. This distance between a number x and 0 is called a number's absolute value. It is shown with the symbol

|x|

If two numbers are at the same distance from 0 as in the case of 10 and -10 they are called opposites. Opposites have the same absolute value since they are both at the same distance from 0.

|10|=10=|−10|

7 0

3 years ago

1. True or false: A function is a rule that assigns each input exactly one

Alexxandr [17]

True a function is a rule that assigns each input exactly one output.

7 0

2 years ago

A man earns $3580 per month and spend 65% of it. How much does he save every month?

Sloan [31]

Answer:

23000 dollars

Step-by-step explanation: because 3580 is about i dont even know scrub

4 0

2 years ago

Lola saved $86.25 in 3 months. She saved $30.75 in the first month and $7.99 in the second month. How much money did Lola save i

ipn [44]

Answer:

$47.51

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

3x^2 + 4x = -8<br> solve using quadratic formula

Firdavs [7]

Use the quadratic equation to solve this (image of the quadratic equation is below)

Remember that quadratic functions are set up like so:

$ax^{2} +bx +c = 0$

To make the equation 3x² + 4x = -8 into a quadratic function you must bring -8 to the left side of the equation so it equals zero. To do this add 8 to both sides

3x² + 4x + 8= -8 + 8

3x² + 4x + 8 = 0

That means that in this equation...

a = 3

b = 4

c = 8

^^^Plug these numbers into the quadratic equation and solve (Keep in mind that +/- is ± )

$\frac{-4+/-\sqrt{(4)^{2}-4(3)(8)}}{2(3)}$