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Mathematics

1 answer:

laila [671]3 years ago

3 0

Answer:

y = -3x + 7

Step-by-step explanation:

Using any 2 pairs of values, say (-3, 16) and (-1, 10), therefore, rate of change of the data given = $\frac{y_2 - y_1}{x_2 - x_1} = \frac{10 - 16}{-1 -(-3} = \frac{-6}{2} = -3$ .

We would get the same rate of change if we use any other two pairs of values in the data given.

Therefore, the data can be modeled by a linear equation because the rate of change remains constant all through.

To represent y as a function of x, find b, since we know the rate of change (m).

Substitute x = -3, y = 16 and m = -3 in y = mx + b.

Thus:

16 = (-3)(-3) + b

16 = 9 + b

Subtract 9 from each side

16 - 9 = b

7 = b

b = 7

Substitute m = -3 and b = 7 in y = mx + b

The function would be:

✅ y = -3x + 7

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f(x) = x4 - 50x2 + 3 (a) Find the intervals on which f is increasing. (Enter the interval that contains smaller numbers first.)

shtirl [24]

Answer:

(-5, 0) ∪ (5, ∞)

Step-by-step explanation:

I find a graph convenient for this purpose. (See below)

When you want to find where a function is increasing or decreasing, you want to look at the sign of the derivative. Here, the derivative is ...

f'(x) = 4x^3 -100x = 4x(x^2 -25) = 4x(x +5)(x -5)

This has zeros at x=-5, x=0, and x=5. The sign of the derivative will be positive when 0 or 2 factors have negative signs. The signs change at the zeros. So, the intervals of f' having a positive sign are (-5, 0) and (5, ∞).