Questions: Do the following for the function g(x) = 6x^2 - 8x + 5 Find m sec for h = 0.5, 0.1, and 0.01 at x = 1. What value does m see approach as h approaches 0?

Solution Steps

To find the secant slope \( m_{\text{sec}} \) for the function \( g(x) = 6x^2 - 8x + 5 \) at \( x = 1 \) with different values of \( h \), we use the formula for the secant slope:

\[ m_{\text{sec}} = \frac{g(x + h) - g(x)}{h} \]

We will calculate this for \( h = 0.5, 0.1, \) and \( 0.01 \), and observe the trend as \( h \) approaches 0.

The secant slope \( m_{\text{sec}} \) is calculated using:

\[ m_{\text{sec}} = \frac{g(x + h) - g(x)}{h} \]

For \( h = 0.5 \):

\[ m_{\text{sec}} = \frac{g(1 + 0.5) - g(1)}{0.5} = \frac{g(1.5) - g(1)}{0.5} = 7.0 \]

For \( h = 0.1 \):

\[ m_{\text{sec}} = \frac{g(1 + 0.1) - g(1)}{0.1} = \frac{g(1.1) - g(1)}{0.1} \approx 4.600 \]

For \( h = 0.01 \):

\[ m_{\text{sec}} = \frac{g(1 + 0.01) - g(1)}{0.01} = \frac{g(1.01) - g(1)}{0.01} \approx 4.060 \]

Final Answer