Question

question 4 (1 point)

determine an expression, in simplified form, for the slope of the secant \\(pq\\) with \\(p(1, 2)\\) and \\(q(1 + h, f(1 + h))\\) where \\(f(x) = 2x^2\\).

\\(8 + 4h\\)
\\(4 + 2h\\)
\\(4 - 2h\\)
\\(8 - 4h\\)

Explanation:

Evaluate the function at the given point

$$ f(1+h) = 2(1+h)^2 = 2(1 + 2h + h^2) = 2 + 4h + 2h^2 $$

Apply the slope formula

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{f(1+h) - 2}{(1+h) - 1} $$

Simplify the expression

$$ m = \frac{(2 + 4h + 2h^2) - 2}{h} = \frac{4h + 2h^2}{h} = 4 + 2h $$

Answer:

• (A) \(8 + 4h\)
• (B) \(4 + 2h\) (Correct answer)
• (C) \(4 - 2h\)
• (D) \(8 - 4h\)