Answer
\[
T(x)=25+1.2 x
\]
Work Step by Step
\[
T^{\prime \prime}(x)=0
\]
Integrate to get
\[
T^{\prime}(x)=C
\]
Again integrate
\[
K+C x=T(x)
\]
$25=T(0),$ so:
\[
\begin{array}{c}
K+C \cdot 0=25 \\
25=K
\end{array}
\]
$85=T(50),$ so:
\[
25+C \cdot 50=85
\]
\[
C \cdot 50=60
\]
Divide each side by 50
\[
C=1.2
\]
