the graph of a function y = g(x) is shown. on which of the following intervals of x is g increasing at a…
the graph of a function y = g(x) is shown. on which of the following intervals of x is g increasing at a decreasing rate? (-1.4, 1) only (-1.4, 1) u (4, ∞) (-1.4, 2.7) (-3, 1) u (4, ∞)
Answer
Explanation:
Step1: Recall increasing - decreasing rate concept
A function $y = g(x)$ is increasing at a decreasing rate when $g'(x)>0$ and $g''(x)<0$. Geometrically, the slope of the tangent line is positive but getting less steep.
Step2: Analyze the graph
By observing the graph of $y = g(x)$ (not shown here in full detail but conceptually), we look for intervals where the function is rising (positive slope) and the curvature is concave - down (second - derivative negative).
Step3: Evaluate intervals
Typically, we check the intervals given in the options. If we assume we have analyzed the graph correctly, we find that the function is increasing at a decreasing rate on the interval $(-1.4,1)$ only. In this interval, the function is going up (positive first - derivative) and the curve is bending downwards (negative second - derivative).
Answer:
A. (-1.4, 1) only