Question

Over which interval is the graph of f(x) = one-halfx2 + 5x + 6 increasing? (–6.5, ∞)

Answer 1

Using the first derivative test, it is found that the graph is increasing on the interval is (-5, ∞).

What is Function?

A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B.

Here, the function is given by:

        f(x)  =   x²/2 + 5x + 6

On differentiating both sides, with respect to x we get

      f'(x) = x + 5

Then, we test the signal of the derivative, which is the first derivative test.

      x + 5 ≥ 0

       x ≥ -5

Thus, It is found that the Function is increasing on the interval is (-5, ∞).

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