Answer:
Literally take your f(x) and - your g(x)
(x^2+9x+18) - (x + 6)
Remember to distribute the negative sign.
Answer: 15e^5x
Step - by - step
y=3e^5x - 2
By the sum rule, the derivative of 3e^5x - 2 with respect to x is d/dx [ 3e^5x ] + d/dx [-2].
d/dx [ 3e^5x ] + d/dx [ -2 ]
Evalute d/dx [ 3e^5x ]
Since 3 is constant with respect to x , the derivative of 3e^5x with respect to x is
3 d/dx [ e^5x ].
3 d/dx [ e^5x ] + d/dx [ -2 ]
Differentiate using the chain rule, which states that d/dx [ f(g(x))] is f' (g(x)) g' (x) where f(x) = e^x and g(x) = 5x.
To apply the Chain Rule, set u as 5x.
3 ( d/du [ e^u] d/dx [5x] ) + d/dx [ -2]
Differentiate using the Exponential rule which states that d/du [ a^u ] is a^u ln(a) where a=e.
3( e^u d/dx[5x] ) + d/dx [ -2 ]
Replace
3(e^5x d/dx [5x] ) + d/dx [ -2 ]
3(e^5x( 5 d/dx [x] )) + d/dx [ -2 ]
Diffentiate using the Power Rule which states that d/dx [x^n] is nx^n-1 where n=1.
3(e^5x(5*1)) + d/dx [-2]
3 ( e^5x * 5 ) + d/dx [-2]
Multiply 5 by 3
15e^5x + d/dx [-2]
Since -2 is constant with respect to x, the derivative of -2 with respect to x is 0.
15e^5x + 0
15e^5x
Answer:
D.) If soccer balls are sold for $2.05 or $14.61 each, the store will break even but will not make a profit.
Step-by-step explanation:
Let us assume x = selling price of each soccer ball
y = daily profit earned from selling of soccer balls
Given that
Y= 
where,
a = -6
b = 100
c = -180
Now we have to applied the formula which is as follows
x 
x^1 = -2.05285
Now
x^2 
x^2 = 14.6138
Based on this the option D is most appropriate as per the given situation
Answer:
(-2, 1)
Step-by-step explanation:
Hi Juliadayx! How are you?
Well, maybe you already heard about the domain and the range of a function.
The domain is the set of values that the independent variable can take (usually referred to as the letter "x"), while the range is the set of values that the dependent variable takes, which is called f(x) or function of x.
In this case, the exercise asks you to evaluate for which values of “x” (right column of the table), the function “f(x)” takes positive values (left column of the table), the positive values also include zero. And in this case you can see that the function f(x) is only positive for the values of "x": -2, -1, 0 and 1. Therefore, the answer is the entire interval (-2, 1).
I hope I've been helpful!
Regards!
