anonymous
  • anonymous
The graph of f ′ (x), the derivative of x, is continuous for all x and consists of five line segments as shown below. Given f (0) = 6, find the absolute maximum value of f (x) over the interval [0, 5].
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
https://i.gyazo.com/3a0c5752c089935dfdb05e7e07aaeb38.png
anonymous
  • anonymous
@jim_thompson5910 Mind checking?
anonymous
  • anonymous
The max value would have to be at that horizontal line no?

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jim_thompson5910
  • jim_thompson5910
They're showing f ' (x) NOT f(x)
jim_thompson5910
  • jim_thompson5910
hint: find the area under the curve from x = 0 to x = 5
anonymous
  • anonymous
So it would be 8?
anonymous
  • anonymous
Wait, find the integral basically?
jim_thompson5910
  • jim_thompson5910
yeah
anonymous
  • anonymous
How would I do that? Should I use geometry?
jim_thompson5910
  • jim_thompson5910
yes that's how I'd do it
jim_thompson5910
  • jim_thompson5910
break it up into 2 triangles and a rectangle or find the area of the trapezoid
anonymous
  • anonymous
First triangle 2*2*1/2
anonymous
  • anonymous
Square 2*2
anonymous
  • anonymous
Second triangle 2*1*1/2
anonymous
  • anonymous
Added them all.
anonymous
  • anonymous
Which actually gives you 7
jim_thompson5910
  • jim_thompson5910
so the net change is 7 meaning that f(5) = f(0) + (net change) f(5) = f(0) + 7 f(5) = 6+7 f(5) = 13 this is the max value of f(x)
anonymous
  • anonymous
Why'd you add the 6?
jim_thompson5910
  • jim_thompson5910
because we know for a fact that f(0) = 6 the graph of f ' says that f is increasing the area under f ' tells us how much f is increasing (in this case at most 7)
jim_thompson5910
  • jim_thompson5910
area under f ' = net change of f(x)

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