Over which interval is the graph of f(x) = 1/2x^2 + 5x + 6 increasing?

(–6.5, ∞)

(–5, ∞)

(–∞, –5)

(–∞, –6.5)

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Verified Answer :

HomertheGenius HomertheGenius · Answer 1 · 2016-07-01T17:20:41-04:00

We will use derivative of this function:
f´(x ) = x + 5
x + 5 > 0
x > -5
The graph is increasing for x ∈ ( - 5, ∞ ).
Answer: B)

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AFOKE88 AFOKE88 · Answer 2 · 2022-06-01T10:37:10-04:00

The interval at which the graph of f(x) = ¹/₂x² + 5x + 6 is increasing is; (–5, ∞)

We are given the function;

f(x) = ¹/₂x² + 5x + 6

We want to find the interval for which the function is increasing and so we first find derivative to get;

f'(x ) = x + 5

For the function to increase, it means f'(x) > 0.

Thus;

x + 5 > 0

x > -5

Thus, the graph is increasing at interval of ( -5, ∞).

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