Question

(a) The altitude of a triangle is increasing at a rate of 1
centimeters/minute while the area of the

triangle is increasing at a rate of 2 square centimeters/minute. At
what rate is the base of the

triangle changing when the altitude is 7 centimeters and the area
is 88 square centimeters?

(b) f(x)=x√x^2+1

defined on the interval −5≤x≤6

f(x) is concave down on the interval *x* = ___ to x
=___

f(x) is concave up on the interval *x* = ___ to x
=___

The inflection point for this function is at *x =
___*

The minimum for this function occurs at *x = ___*

The maximum for this function occurs at *x* = ___

(c) f(x)=12x^5+75x^4−120x^3+3

f(x) has inflection points at (reading from left to right)
*x* = *D*, *E*, and *F
*

where *D* is ____ and *E* is *____* and
*F* is ____

Answer #1

The altitude of a triangle is increasing at a rate of
1 centimeters/minute while the area of the triangle is increasing
at a rate of 5 square centimeters/minute. At what rate is the base
of the triangle changing when the altitude is 12 centimeters and
the area is 85 square centimeters?
________cm/min

The altitude (i.e., height) of a triangle is increasing at a
rate of 1.5 cm/minute while the area of the triangle is increasing
at a rate of 2.5 square cm/minute. At what rate is the base of the
triangle changing when the altitude is 11.5 centimeters and the
area is 87 square centimeters?

The altitude (height) of a triangle is increasing at a rate of 1
cm/min while the area of the triangle is increasing at a rate of 2
square cm per min. At what rate is the base of the triangle
changing when the altitude is 10 cm and the area is 100 square
cm?

The
altitude of a triangle is increasing at a rate of 2.5 cm/min
while the area the triangle is increasing at a rate of 2.5 cm² per
minute. At what rate is the base of the triangle changing when the
altitude is 8.5 cm and the area is 94 cm² ?

The altitude of a triangle is increasing at a rate of 1 cm/min
while the area of the triangle is increasing at a rate of 2
cm2/min.
At what rate is the base of the triangle changing when the altitude
is 20 cm and the area is 160 cm2?

1. The critical point(s) of the function
2. The interval(s) of increasing and decreasing
3. The local extrema
4. The interval(s) of concave up and concave down
5. The inflection point(s).
f(x) = (x^2 − 2x + 2)e^x

The height of a triangle is decreasing at a rate of 1 cm/min
while its area is increasing at a rate of 2 cm^2/min.
(a) What is the base of the triangle when its height is 10 cm
and its area is 100 cm^2?
(b) At what rate is the base of the triangle changing when its
height is 10 cm and its area is 100cm^2?

Let f(x)=4+12x−x^3. Find (a) the intervals on which ff is
increasing, (b) the intervals on which ff is decreasing, (c) the
open intervals on which ff is concave up, (d) the open intervals on
which f is concave down, and (e) the x-coordinates of all
inflection points.
(a) f is increasing on the interval(s) =
(b) f is decreasing on the interval(s) =
(c) f is concave up on the open interval(s) =
(d) f is concave down on the...

. Let f(x) = 3x^5/5 −2x^4+1. Find the following:
(a) Interval of increasing:
(b) Interval of decreasing:
(c) Local maximum(s) at x =
d) Local minimum(s) at x =
(e) Interval of concave up:
(f) Interval of concave down:
(g) Inflection point(s) at x =

1.f(x)= e-2^(x)
a. Give in interval notation the intervals where is increasing
and where is decreasing.
b. Give in interval notation the intervals where is concave up
and where is concave down.
c. Give the coordinates of any points of inflection.
d. Sketch the curve

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