Can someone explain to me what a “derivative” means? How do you find the derivative of f(x)=x^3+1?

1 answer:

4 0

The derivative is the rate of change of a function, basically represents the slope at different points. To find the derivative of the given function you can use the power rule, which means, if n is a real number, d/dx(x^n)= nx^(n-1). This is a simplification of the chain rule based on the fact that d/dx(x)=1. Anyway, this means that d/dx(x^3 + 1)= 3x^2. Here n is 3 and so it is 3*x^(3-1)= 3x^2. The derivative of x^3+1 is 3x^2.

If you are wondering what happened to the 1, for any constant C, d/dx(C)=0.

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Carlotta subscribes to the HotBurn music service. She can download no more than 12 song files per week. Carlotta has already dow

UNO [17]

Answer:

Inequality: $x+10\leq 12$

Inequality solved: $x\leq 2$

The graph is attached.

Step-by-step explanation:

You need to remember the meaning of the inequalities symbols:

: Less than.

$>$ : Greater than.

$\leq$ : Less than or equal to.

$\geq$ : Greater than or equal to.

Let be "x" the number of more songs Carlotta can download.

According to the information given in the exercise, she can download no more than 12 song files per week. This indicates that you must use the symbol $\leq$ .

Since she has already downloaded 10 song files this week, you can write the following inequality that represents this situation:

$x+10\leq 12$

In order to solve it, you must subtract 10 from both sides:

$x+10-10\leq 12-10\\\\x\leq 2$