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

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Answer 1 · 2018-06-30T00:51:35

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

By definition, a function #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!