for the function $f(x)=2x^{2}-5x - 8$, find the slope of the secant line between $x = 3$ and $x = 5$.
for the function $f(x)=2x^{2}-5x - 8$, find the slope of the secant line between $x = 3$ and $x = 5$.
Answer
Explanation:
Step1: Find (f(3))
Substitute (x = 3) into (f(x)=2x^{2}-5x - 8). [ \begin{align*} f(3)&=2\times3^{2}-5\times3 - 8\ &=2\times9-15 - 8\ &=18-15 - 8\ &=-5 \end{align*} ]
Step2: Find (f(5))
Substitute (x = 5) into (f(x)=2x^{2}-5x - 8). [ \begin{align*} f(5)&=2\times5^{2}-5\times5 - 8\ &=2\times25-25 - 8\ &=50-25 - 8\ &=17 \end{align*} ]
Step3: Calculate the slope of the secant line
The slope (m) of the secant line between two points ((x_1,y_1)) and ((x_2,y_2)) is (m=\frac{y_2 - y_1}{x_2 - x_1}). Here (x_1 = 3,y_1=f(3)=-5,x_2 = 5,y_2=f(5)=17). [ \begin{align*} m&=\frac{f(5)-f(3)}{5 - 3}\ &=\frac{17-(-5)}{2}\ &=\frac{17 + 5}{2}\ &=\frac{22}{2}\ &=11 \end{align*} ]
Answer:
11