Question

answer the following questions about ( f(x)=4x + 140 ).
(a) calculate the change in ( f(x) ) from ( x = 13 ) to ( x = 18 ).
(b) graph ( f^{prime}(x) ) and use geometric formulas to calculate the area between the graph of ( f^{prime}(x) ) and the x - axis from ( x = 13 ) to ( x = 18 ).
(a) calculate the change in ( f(x) ) from ( x = 13 ) to ( x = 18 ).
the change is ( square ).
(simplify your answer.)

Explanation:

Step1: Calculate \( F(18) \)

Substitute \( x = 18 \) into \( F(x)=4x + 140 \).
\( F(18)=4\times18+140=72 + 140=212 \)

Step2: Calculate \( F(13) \)

Substitute \( x = 13 \) into \( F(x)=4x + 140 \).
\( F(13)=4\times13+140=52+140 = 192 \)

Step3: Calculate the change in \( F(x) \)

The change in \( F(x) \) from \( x = 13 \) to \( x = 18 \) is \( F(18)-F(13) \).
\( F(18)-F(13)=212 - 192=20 \)

Answer:

\( 20 \)