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makvit [3.9K]
2 years ago
7

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

Mathematics
1 answer:
juin [17]2 years ago
7 0

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

<h3>What is Function?</h3>

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, ∞).

Learn more about Function from:

brainly.com/question/12431044

#SPJ1

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Simplify (x^2)^3*5x/6x^2*15x^3
nasty-shy [4]

When we Simplify [(x^2)^3 × 5x] / [6x^2 × 15x^3], the result obtained is (1/18)x^2

<h3>Data obtained from the question</h3>
  • [(x^2)^3 × 5x] / [6x^2 × 15x^3]
  • Simplification =?

<h3>How to simplify [(x^2)^3 × 5x] / [6x^2 × 15x^3]</h3>

[(x^2)^3 × 5x] / [6x^2 × 15x^3]

Recall

(M^a)^b = M^ab

Thus,

(x^2)^3 = x^6

  • [(x^2)^3 × 5x] / [6x^2 × 15x^3] = [x^6 × 5x] / [6x^2 × 15x^3]

Recall

M^a × M^b = M^(a+b)

Thus,

x^6 × 5x = 5x^(6 + 1) = 5x^7

6x^2 × 15x^3] = (6×15)x^(2 + 3) = 90x^5

  • [x^6 × 5x] / [6x^2 × 15x^3] = 5x^7 / 90x^5

Recall

M^a ÷ M^b = M^(a - b)

Thus,

5x^7 ÷ 90x^5 = (5÷90)x^(7 - 5) = (1/18)x^2

Therefore,

  • [(x^2)^3 × 5x] / [6x^2 × 15x^3] = (1/18)x^2

Learn more about algebra:

brainly.com/question/2768008

#SPJ1

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