How do you determine the intervals where $f (x) = 3 x - 4$ $f(x)=3x-4$ is concave up or down?

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Answer 1 · 2018-06-30T00:51:35

$f (x) = 3 x - 4$ $f(x) = 3x-4$ is never concave up or concave down.

By definition, a function $f (x)$ $f(x)$ is concave up when $f''(x) > 0$ , and it is concave down when $f''(x) < 0$ .

Let $f(x) = 3x - 4$ .

$f'(x) = 3$

$f''(x) = 0$

Here, we notice that the second derivative is never greater than or less than 0, which means $f(x) = 3x-4$ is never concave up or concave down.

Answer 2 · 2018-06-30T00:58:02

Neither- point of inflection

When we want to determine if a function is concave up or concave down, we want to analyze the function's second derivatives

$f'(x)=3$

$f''(x)=0$ (Derivative of a constant is zero)

We have three possible scenarios:

We see that our second derivative of $f(x)$ is zero, which means we are in scenario three:

$f(x)$ is neither concave up nor down...we have a point of inflection.

Hope this helps!

How do you determine the intervals where f(x)=3x-4f(x)=3x−4f(x)=3x-4 is concave up or down?