Solve the nonlinear inequality. express the solution using interval notation. (x − 2)(x + 8) < 0 webassign

1 answer:

8 0

First you find the zeros/x-intercepts using the factors already given in the inequality.

$x = 2$
$x = - 8$

Therefore we make our solution using the interval notation.

$- 8 \leqslant x \leqslant 2$

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Given that f(–2.4) = -1 and f(-1.9) = -8, approximate f'(-2.4). f'(-2.4)

lora16 [44]

Answer:

f'(-2.4) ≈ -14

General Formulas and Concepts:
Algebra I

Coordinate Planes

Coordinates (x, y)

Slope Formula: $\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}$

Functions

Function Notation

Calculus

Differentiation

Derivatives
Derivative Notation

Step-by-step explanation:

*Note:

The definition of a derivative is the slope of the tangent line.

Step 1: Define

Identify.

f(-2.4) = -1

f(-1.9) = -8

Step 2: Differentiate

Simply plug in the 2 coordinates into the slope formula to find slope m.

[Derivative] Set up [Slope Formula]: $\displaystyle f'(-2.4) \approx \frac{f(x_2) - f(x_1)}{x_2 - x_1}$
Substitute in coordinates: $\displaystyle f'(-2.4) \approx \frac{-8 - -1}{-1.9 - -2.4}$
Evaluate: $\displaystyle f'(-2.4) \approx -14$