Estimate the slope of the tangent line to the curve f(x) = x2 at the point (1, f(1)) by examining the trend in the secant slopes calculated.

f'(1) = 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Calculus

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

Derivative Notation

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

f(x) = x²

Point (1, f(1))

Step 2: Differentiate

Step 3: Find Slope

Use the point (1, f(1)) to find the instantaneous slope

This tells us that at point (1, f(1)), the slope of the tangent line is 2. We can write an equation using point slope form as well: y - f(1) = 2(x - 1)

21.4 i did it already for s1

step-by-step explanation:

$4034.40

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40