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The graph of f ′ (x), the derivative of f of x, is continuous for all x and consists of five line segments as shown below. Given f (0) = 7, find the absolute minimum value of f (x) over the interval [–3, 0].
A. 0
B. 2.5
C. 4.5
D. 11.5

The graph of f x the derivative of f of x is continuous for all x and consists of five line segments as shown below Given f 0 7 find the absolute minimum value class=

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MathPhys

Answer:

B

Step-by-step explanation:

f(0) - f(-3) = area under f'(x) from x=0 to x=3.

We can find the area under f'(x) in this interval by finding the area of the triangle formed by the line.

A = 1/2 b h

A = 1/2 (3) (3)

A = 4.5

f(0) - f(-3) = 4.5

Since f(0) = 7:

7 - f(-3) = 4.5

f(-3) = 7 - 4.5

f(-3) = 2.5