#### To determine

**To find:**

g''4

#### Answer

-2

#### Explanation

**1) Concept:**

Use the formula of slope of line,

dydx=y2-y1x2-x1

**2) Given:**

gx=∫0xf(t)dt

**3) Calculation:**

It is from exercise 9,

gx=∫0xf(t)dt,

Differentiate with respect to x,

ddxgx=ddx∫0xf(t)dt

By Fundamental Theorem of Calculus,

g'x=fx

Again differentiate

g''x=f'x

Substitute x=4,

g''4=f'4

So, f'4 is the slope of line segment at x=4

Use the formula of slope,

f'4=y2-y1x2-x1

Take any two points on that line segment

3, 25, -2

f'4=-2-25-3

=-42

=-2

So, g''4=-2

**Conclusion:**

Therefore,

g''4=-2