Question

The equation of a curve is y = x³ + 4x. Show that the value of y increases when x increases. ² is a decreasing function.​

Answer 1

We will see that f'(x) > 0, which means that f(x) is an increasing function.

How to prove that the function is increasing?

For any function f(x), if f'(x) > 0, then f(x) is increasing for any value of x.

Here we have the cubic function:

f(x) = x³ + 4x

If we differentiate this, we get:

f'(x) = df(x)/dx = 3x² + 4.

And notice that x² is always positive, then f'(x) > 0, which means that f(x) is an increasing function.

If you want to learn more about cubic functions:

brainly.com/question/20896994

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