Question

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].

Answer 1

https://i.gyazo.com/3a0c5752c089935dfdb05e7e07aaeb38.png

Answer 2

@jim_thompson5910 Mind checking?

Answer 3

The max value would have to be at that horizontal line no?

Answer 4

They're showing f ' (x)

NOT f(x)

Answer 5

hint: find the area under the curve from x = 0 to x = 5

Answer 6

So it would be 8?

Answer 7

Wait, find the integral basically?

Answer 8

yeah

Answer 9

How would I do that? Should I use geometry?

Answer 10

yes that's how I'd do it

Answer 11

break it up into 2 triangles and a rectangle
or find the area of the trapezoid

Answer 12

First triangle 2*2*1/2

Answer 13

Square 2*2

Answer 14

Second triangle 2*1*1/2

Answer 15

Added them all.

Answer 16

Which actually gives you 7

Answer 17

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)

Answer 18

Why'd you add the 6?

Answer 19

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)

Answer 20

area under f ' = net change of f(x)