Question

webwork 2 - topics 4 - 5: problem 4 (1 point) the tangent line to y = f(x) at (-1,2) passes through the point (7,2). compute the following: a.) f(-1)= b.) f(-1)= note: you can earn partial credit on this problem. preview my answers submit answers you have attempted this problem 0 times. you have 6 attempts remaining.

Explanation:

Step1: Recall function - value at a point

The point $(-1,2)$ lies on the curve $y = f(x)$. By the definition of a function, if the point $(x_0,y_0)$ lies on the curve $y = f(x)$, then $f(x_0)=y_0$. Here $x_0=-1$ and $y_0 = 2$, so $f(-1)=2$.

Step2: Recall the slope of the tangent - line

The slope of the tangent line to the curve $y = f(x)$ at the point $(x_0,y_0)$ is given by $f^{\prime}(x_0)$. The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. The tangent line to $y = f(x)$ at $(-1,2)$ passes through $(-1,2)$ and $(7,2)$. Using the slope formula with $x_1=-1,y_1 = 2,x_2=7,y_2 = 2$, we have $m=\frac{2 - 2}{7-(-1)}=0$. Since the slope of the tangent line at $x=-1$ is $f^{\prime}(-1)$, then $f^{\prime}(-1)=0$.

Answer:

a. $2$
b. $0$