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