Question

according to a study, a vehicles fuel economy, in miles per gallon (mpg), decreases rapidly for speeds over 40 mph.
a) estimate the speed at which the absolute maximum fuel economy is obtained.
b) estimate the speed at which the absolute minimum fuel economy is obtained.
c) what is the fuel economy obtained at 95 mph?

a) the speed at which the absolute maximum fuel economy is obtained is approximately \\(\boldsymbol{\square}\\)
(type a whole number.)
b) the speed at which the absolute minimum fuel economy is obtained is approximately \\(\boldsymbol{\square}\\)
(type a whole number.)
c) the fuel economy obtained at 95 mph is \\(\boldsymbol{\square}\\)
(type a whole number.)

Explanation:

Step1: Analyze the graph for absolute maximum

The graph of fuel economy (mpg) vs speed (mph) has a peak. The absolute maximum occurs at the highest point of the curve. Looking at the x - axis (speed) values, the peak seems to be around 45 mph (by visually inspecting the graph where the curve reaches its highest point).

Step2: Analyze the graph for absolute minimum

The absolute minimum on the graph (since the curve ends at 95 mph with fuel economy approaching 0, but we check the domain). The right - most point of the graph (highest speed shown) is 95 mph, and the fuel economy there is near 0, but also, we see the trend. The absolute minimum in the given domain (from around 0 to 95 mph) occurs at the right - most point, 95 mph? Wait, no, wait. Wait, the graph starts at some speed and goes to 95. Wait, actually, looking at the x - axis labels: 0,5,15,25,35,45,55,65,75,85,95. The curve rises to a peak and then falls. The absolute minimum in the interval (from the start to 95 mph) would be at the end - point 95 mph? Wait, no, maybe I misread. Wait, the problem says "for speeds over 40 mph, fuel economy decreases rapidly". The graph: let's see the x - axis is speed (mph), y - axis is fuel economy (mpg). The curve increases from left (low speed) to a peak, then decreases. So the absolute maximum is at the peak, absolute minimum is at the right - most point (95 mph) or maybe the left - most? Wait, no, at low speed, the fuel economy is, say, around 20? Wait, no, looking at the y - axis: 0,9,15,20,24,30,36. Wait, the left - most part: at speed 0? No, the first label is 0, then 5, etc. Wait, maybe the x - axis starts at 0? Wait, the graph: let's assume the x - axis is speed (mph) from 0 to 95, y - axis fuel economy (mpg) from 0 to 36. The curve: starts at some point, rises to a peak, then falls. So:

a) Absolute maximum: the peak of the curve. Looking at the x - value of the peak. The x - axis ticks: 0,5,15,25,35,45,55,65,75,85,95. The peak is around x = 45 (since between 35 and 55, the peak is at 45? Let's check the graph. So the speed at absolute maximum is approximately 45 mph.

b) Absolute minimum: the lowest point on the graph. The graph ends at x = 95, and at x = 95, the y - value is 0? Wait, the y - axis at x = 95: the curve meets the x - axis? So the absolute minimum in the domain (from the start to 95 mph) is at x = 95 mph? Wait, but the problem says "estimate the speed at which absolute minimum is obtained". So if the curve falls all the way to 0 at 95 mph, then the absolute minimum is at 95 mph? But wait, maybe I made a mistake. Wait, no, let's re - examine.

c) For 85 mph: look at the x - axis, 85 mph. Find the y - value (fuel economy) at x = 85. From the graph, at x = 85, the y - value (fuel economy) is, say, 9? Wait, no, let's see the y - axis: 0,9,15,20,24,30,36. At x = 85, the curve is at y = 9? Wait, no, maybe 9? Wait, let's do step by step.

a) Absolute maximum: the peak of the fuel economy curve. Looking at the x - axis, the peak is around 45 mph (since the x - ticks are 0,5,15,25,35,45,55,... and the peak is at 45? Wait, 35,45,55: the peak is between 35 and 55, and the x - tick at 45 is the middle. So we estimate 45 mph.

b) Absolute minimum: the lowest fuel economy. The curve goes from a peak down to near 0 at 95 mph. So the absolute minimum in the given range (from the start to 95 mph) is at 95 mph? Wait, but the problem says "type a whole number". Wait, maybe I misread the graph. Wait, the x - axis at 95 mph, the y - axis is 0? So the speed at absolute minimum is 95 mph?

c) At 85 mph: look at the x - axis, 85 mph. The y - value (fuel economy) at x = 85: from the graph, the point at x = 85 is at y = 9? Wait, the y - axis has 9 as a label. So we estimate 9 mpg.

Wait, let's confirm:

a) The peak of the curve (absolute maximum) is at x = 45 mph (by looking at the graph, the highest point is around x = 45).

b) The absolute minimum: since the curve decreases after the peak, and the right - most point is 95 mph, where the fuel economy is the lowest (closest to 0), so the speed is 95 mph.

c) At 85 mph, looking at the graph, the fuel economy is 9 mpg (since the y - axis at 85 mph is at the 9 mpg mark? Wait, the y - axis labels: 0,9,15,20,24,30,36. So at x = 85, the y - value is 9.

Answer:

a) 45
b) 95
c) 9