current attempt in progress\nuse the figure to fill in the blanks in the following statements about the…
current attempt in progress\nuse the figure to fill in the blanks in the following statements about the function f at point a.\n(a) f( ) = \n(b) f( ) = \n(7,3) a\n(7.2,3.8)\ntangent line\nf(x)\netextbook and media\nsave for later\nusing multiple attempts will impact your score.\n5% score reduction after attempt 5\nattempts: 0 of 15 used submit answer
Answer
Explanation:
Step1: Recall function - value definition
The value of the function $y = f(x)$ at a point $x=a$ is the $y$-coordinate of the point on the graph of the function with $x$-coordinate $a$. At point $A=(7,3)$ on the graph of $y = f(x)$, when $x = 7$, $y=f(7)=3$.
Step2: Recall derivative - slope relationship
The derivative of the function $y = f(x)$ at a point $x=a$, $f^{\prime}(a)$, is the slope of the tangent line to the graph of $y = f(x)$ at $x = a$. The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. The tangent - line to $y = f(x)$ at $x = 7$ passes through the points $(7,3)$ and $(7.2,3.8)$. So, $m=f^{\prime}(7)=\frac{3.8 - 3}{7.2 - 7}=\frac{0.8}{0.2}=4$.
Answer:
(a) $f(7)=3$ (b) $f^{\prime}(7)=4$