question\nfind the slope of the secant line between (x = - 2) and (x = 2) on the graph of the function…
question\nfind the slope of the secant line between (x = - 2) and (x = 2) on the graph of the function (f(x)=5x^{3}-x^{2}-5x - 3).\nprovide your answer below:
Answer
Answer:
17
Explanation:
Step1: Find (f(-2))
[ \begin{align*} f(-2)&=5(-2)^{3}-(-2)^{2}-5(-2)-3\ &=5\times(-8)-4 + 10-3\ &=-40-4 + 10-3\ &=-37 \end{align*} ]
Step2: Find (f(2))
[ \begin{align*} f(2)&=5(2)^{3}-(2)^{2}-5(2)-3\ &=5\times8-4-10 - 3\ &=40-4-10-3\ &=23 \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=-2,y_1 = f(-2)=-37,x_2 = 2,y_2=f(2)=23). [ \begin{align*} m&=\frac{f(2)-f(-2)}{2-(-2)}\ &=\frac{23-(-37)}{2 + 2}\ &=\frac{23 + 37}{4}\ &=\frac{60}{4}\ &=17 \end{align*} ]