Chapter 1.

1.1 Problem Statement

{4,6,8}
{3,5,7,9}

Find an equation of the tangent line at the point specified.

y = $a·sin(x) + $c·cos(x), x = 0

1.2 Step 1

Question 1.1

Recall that a tangent line to a graph of y = f(x) at a point P(a, f(a)) is the line through the point P of slope NsDvRziYBBEox5msqhXYNvE2PJWil8aGpRgA1g==. The equation of the tangent line in point-slope form is

y -wPah0ewYTHV1gRKzC8auX7tZI0q0wCSsWA8Elg== = NsDvRziYBBEox5msqhXYNvE2PJWil8aGpRgA1g==(x-a).

Correct.
Incorrect.

1.3 Step 2

We find the formula for the slope of the tangent line to the graph of y = f(x) for any value of x by calculating f'(x).

Question Sequence

Question 1.2

f(x) = $a·sin(x) + $c·cos(x)

= nc1ItEz0kR4=· + SFgqQUkJGdg= ·

Correct.
Incorrect.

Question 1.3

= $a · +oE3dexu+YXOG8QKjTROFi4zaMs= - $c · 6LVZ3Izit10N+67n+zs4eU+LiGc=

(Note the coefficient on the second answer box is -$c, not $c.)

Correct.
Incorrect.

1.4 Step 3

Question Sequence

Question 1.4

The slope of the tangent line to the graph is given by f'(x) = $a·cos(x) − $c·sin(x). The slope of this line at x = 0 is found by evaluating f'(0).

f'(x) = $a·cos(x) - $c·sin(x)

f'(0) = nc1ItEz0kR4=

Correct.
Incorrect.

Question 1.5

Aside from the slope of the tangent line at x = 0, we also need the point that the line passes through on the graph of f(x). Since this line is tangent to f(x) at x = 0, the point needed is (0, f(0)).

Find f(0).

f(x) = $a·sin(x) + $c·cos(x)

f(0) = SFgqQUkJGdg=

Correct.
Incorrect.

1.5 Step 3

Question Sequence

Question 1.6

Find the equation of the tangent line to f(x) of slope $a at the point (0, $c).

y - f(0) = f'(0)(x-0)

y - SFgqQUkJGdg= = nc1ItEz0kR4= · (x-0)

Correct.
Incorrect.

Question 1.7

y = nc1ItEz0kR4= ·x + SFgqQUkJGdg=

Correct.
Incorrect.