refer to the graph at the right to answer the following questions. (a) at which labeled points is the…

refer to the graph at the right to answer the following questions. (a) at which labeled points is the function increasing? (b) at which labeled points is the graph concave up? (c) which labeled point has the most negative slope? the function is increasing at the labeled point(s) . (use a comma to separate answers as needed.) the graph is concave up at the labeled point(s) . (use a comma to separate answers as needed.) the graph has the most negative slope at the labeled points(s) . (use a comma to separate answers as needed.)

refer to the graph at the right to answer the following questions. (a) at which labeled points is the function increasing? (b) at which labeled points is the graph concave up? (c) which labeled point has the most negative slope? the function is increasing at the labeled point(s) . (use a comma to separate answers as needed.) the graph is concave up at the labeled point(s) . (use a comma to separate answers as needed.) the graph has the most negative slope at the labeled points(s) . (use a comma to separate answers as needed.)

Answer

Explanation:

Step1: Recall increasing - function condition

A function $y = f(x)$ is increasing when $f'(x)>0$. Looking at the graph, the function is increasing where the slope of the tangent line is positive. Points A and F have positive - sloped tangent lines.

Step2: Recall concave - up condition

A function $y = f(x)$ is concave up when $f''(x)>0$, which means the first - derivative $f'(x)$ is increasing. Points C, D, E, F have the graph curving upwards.

Step3: Recall slope condition

The slope of the tangent line to the function $y = f(x)$ at a point is given by $f'(x)$. The most negative slope means the steepest downward - sloping tangent line. Point B has the steepest downward - sloping tangent line among the labeled points.

Answer:

A,F C,D,E,F B