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.
To solve for x, first you need to isolate all x terms on the same side so:
you start with 5 + 4x = 54 - 3x
subtract 5 from both sides to get 5 onto the left side
now you should have 4x = 49 - 3x
now add 3x to both sides to get 3x onto the right side
now you should have 7x = 49
now that you have your x on one side you can solve this like a regular one step equation and divide both sides by 7
this leads you to your answer of x = 7
hope this helps!
Answer:
10y-30
Step-by-step explanation:
10*1y=10y
-3*10=-30
10y-30
Hey there! :)
Answer:
y = 11.
Step-by-step explanation:
Set both of the equations equal:
5x - 9 = x² - 3x + 7
Rearrange the equation:
0 = x² - 3x - 5x + 9 + 7
Combine like terms:
0 = x² - 8x + 16
Factor:
0 = (x -4)²
Solve for x:
0 = x - 4
x = 4.
Plug this into an equation to solve for 'y':
y = 5(4) - 9
y = 20 - 9
y = 11.
Answer:
z ≥ -5/6
Step-by-step explanation:
10z - 2 ≥ 4z - 7
6z ≥ -5
z ≥ -5/6
