Amelia runs a farm stand that sells strawberries and peaches. Each pound of strawberries sells for $1 and each pound of peaches
2 answers:
You might be interested in
Answer:
See Below.
Step-by-step explanation:
We are given the graph of <em>y</em> = f'(x) and we want to determine the characteristics of f(x).
Part A)
<em>f</em> is increasing whenever <em>f'</em> is positive and decreasing whenever <em>f'</em> is negative.
Hence, <em>f</em> is increasing for the interval:
And <em>f</em> is decreasing for the interval:
Part B)
<em>f</em> has a relative maximum at <em>x</em> = <em>c</em> if <em>f'</em> turns from positive to negative at <em>c</em> and a relative minimum if <em>f'</em> turns from negative to positive to negative at <em>c</em>.
<em>f'</em> turns from positive to negative at <em>x</em> = -2 and <em>x</em> = 1.
And <em>f'</em> turns from negative to positive at <em>x</em> = -1 and <em>x</em> = 3.
Hence, <em>f</em> has relative maximums at <em>x</em> = -2 and <em>x</em> = 1, and relative minimums at <em>x</em> = -1 and <em>x</em> = 3.
Part C)
<em>f</em> is concave up whenever <em>f''</em> is positive and concave down whenever <em>f''</em> is negative.
In other words, <em>f</em> is concave up whenever <em>f'</em> is increasing and concave down whenever <em>f'</em> is decreasing.
Hence, <em>f</em> is concave up for the interval (rounded to the nearest tenths):
And concave down for the interval:
Part D)
Points of inflections are where the concavity changes: that is, <em>f''</em> changes from either positive to negative or negative to positive.
In other words, <em>f </em>has an inflection point wherever <em>f'</em> has an extremum point.
<em>f'</em> has extrema at (approximately) <em>x</em> = -1.5, 0, and 2.2.
Hence, <em>f</em> has inflection points at <em>x</em> = -1.5, 0, and 2.2.
I'm not sure what level of math you are at, so I hope it's alright that I used the trig function of tangent. Basically, you just have to find the second base to be able to find the area using the formula for the area of a trapezoid (A = ½h(b₁ + b₂)). To do this, use the information given and a little creativity to create a triangle and find the missing pieces. Finally, plug everything into the equation and voilà. Hope that helps!
"A dilation centered at the origin with scale factor to 1/2 from the origin" means that we must join O to all the vertices of the triangle, and make the distances 1/2 of the original triangle. This is shown clearly in the picture.
The coordinates of the new triangle are A'(0,4), B'(1,-1), C'(-1,-1).
<span>
The relationship between corresponding sides in terms of their lengths:
The sides of the dilated triangle are half the length of the first triangle.
</span><span>The relationship between corresponding sides in terms of their orientations.
The two triangles have the same orientation.
</span><span>The relationship between corresponding angles in terms of their measures.
The two triangles have congruent corresponding angles.</span>
The coordinates of the new triangle are A'(0,4), B'(1,-1), C'(-1,-1).
<span>
The relationship between corresponding sides in terms of their lengths:
The sides of the dilated triangle are half the length of the first triangle.
</span><span>The relationship between corresponding sides in terms of their orientations.
The two triangles have the same orientation.
</span><span>The relationship between corresponding angles in terms of their measures.
The two triangles have congruent corresponding angles.</span>