Question

. Use a calculator or a graphing program to find the slope of the tangent line to the point

Answer 1

`\begin{gathered} m=M((19)/(10))=\frac{57\sqrt[10]{10}\cdot19^{(9)/(10)}}{50} \\ m=20.313 \end{gathered}`

Explanation:

The slope of the tangent line is given at the first derivate of the function, evaluated at x=x0. The value of the function at the given point:

`\begin{gathered} p(x)=6(1.9)^(1.9) \\ p((19)/(10))=\frac{57\sqrt[10]{10}\cdot19^{(9)/(10)}}{50} \end{gathered}`

Therefore,

`\begin{gathered} p(x)=6x^(1.9) \\ p^(\prime)(x)=\frac{57x^{(9)/(10)}}{5} \end{gathered}`

Then, for the following function the slope of the tangent line is:

`\begin{gathered} M(x)=p^(\prime)(x)=\frac{57x^{(9)/(10)}}{5} \\ \text{Then,} \\ m=M((19)/(10))=\frac{57\sqrt[10]{10}\cdot19^{(9)/(10)}}{50} \end{gathered}`