2.
3/3 points |
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SCalcET8 2.7.003.
Consider the parabola
y
=
6
x
−
x
2
.
(a) Find the slope of the tangent line to the parabola at the point (
1
,
5
).
4
(b) Find an equation of the tangent line in part (a).
y
=
$$4
x
+1
(c) Graph the parabola and the tangent line.

6/5/2019
hw06S2.7
3.
2/3 points |
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SCalcET8 2.7.029.
(a) If
find
F '
(
3
) and use it to find an equation of the tangent line to the curve
at the point (
3
,
3
).

3/7
(b) Illustrate part (a) by graphing the curve and the tangent line on the same screen.

6/5/2019
hw06S2.7
4/7
4.
4/4 points |
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SCalcET8 2.7.022.
If the tangent line to
y
=
f
(
x
) at (
7
,
6
) passes through the point (0,
5
), find
f
(
7
) and
f '
(
7
).
f
(
7
) =
$$6
f '
(
7
) =
$$17

6/5/2019
hw06S2.7
5/7
5.
8/8 points |
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An object is moving around the unit circle with parametric equations
x(t)=cos(t), y(t)=sin(t)
, so it's location at time
t
is
P(t)=
(cos(t),sin(t))
. Assume
0 < t <
π
/2
. At a given time
t
, the tangent line to the unit circle at the position
P(t)
will determine a right
triangle in the first quadrant. (Connect the origin with the
y
intercept and
x
intercept of the tangent line.)
The identity