Question

graph the function (f(x) = -2x^2) and draw the tangent line to the graph at (x = -2).

a. simplify the difference quotient.

(\frac{f(x+h) - f(x)}{h} = )

b. find the derivative of (f(x)) by applying the definition.

(lim_{h \to 0} \frac{f(x+h) - f(x)}{h} = )

c. find the slope of the tangent line at (x = -2). this slope is the same as the line drawn on the grid.

Explanation:

Simplify the difference quotient

$$
LATEXBLOCK0
$$

Apply the derivative definition

$$
LATEXBLOCK1
$$

Calculate the tangent slope at \(x = -2\)

$$
LATEXBLOCK2
$$

Answer:

Question A

The simplified difference quotient is <blank>\(-4x - 2h\)</blank>.

Question B

The derivative of \(f(x)\) by applying the definition is <blank>\(-4x\)</blank>.

Question C

The slope of the tangent line at \(x = -2\) is <blank>8</blank>.