Problem Statement

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

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

y = 3·sin(x) + 4·cos(x), x = 0

 
Step 1

Question 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 . The equation of the tangent line in point-slope form is

y - = (x-a).

Correct.
Incorrect.

 
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 2

f(x) = 3·sin(x) + 4·cos(x)

= · + ·

Correct.
Incorrect.

Question 3

= 3 · - 4 ·

Correct.
Incorrect.

 
Step 3

Question Sequence

Question 4

The slope of the tangent line to the graph is given by f'(x) = 3·cos(x) − 4·sin(x). The slope of this line at x = 0 is found by evaluating f'(0).

f'(x) = 3·cos(x) - 4·sin(x)

f'(0) =

Correct.
Incorrect.

Question 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) = 3·sin(x) + 4·cos(x)

f(0) =

Correct.
Incorrect.

 
Step 3

Question Sequence

Question 6

Find the equation of the tangent line to f(x) of slope 3 at the point (0, 4).

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

y - = · (x-0)

Correct.
Incorrect.

Question 7

y = ·x +

Correct.
Incorrect.