#### To determine

**To find:**

The interval where F is concave downward

#### Answer

(-1, 1)

#### Explanation

**1) Concept:**

i) The Fundamental Theorem of Calculus:

If f is continuous on [a, b], then the function g defined by

gx=∫axf(t)dt a≤x≤b

is continuous on [a, b] and differentiable on (a,b), and g'x=f(x)

ii)

If f''x<0 for all x in an interval I, the graph of f is concave downward on I

**2) Given:**

Fx=∫1xftdt

**3) Calculations:**

By using Fundamental Theorem of Calculus,

F'x=f(x)

Again differentiating,

F''x=f'(x)

From the given graph in interval -1, 1 he graph of f is decreasing hence f’(x)<0 that is F’’(x)<0 in -1, 1 . Hence by definition of concavity F is concave downward within interval (-1, 1)

**Conclusion:**

Therefore, the function is concave down on interval (-1, 1).