Find the domain intercepts and turning points of the functio

Find the domain, intercepts, and turning points of the function defined by the graph. domain [-7, 7] (Enter your answer using interval notation.) x-intercepts (x, y) = (3, 0) (smaller x-value) (x, y) = (6, 0) (larger x-value) y-intercept (x, y) = (0, 8) x-coordinates of turning point(s) x = 1, 3, 5 (Enter your answers as a comma-separated list.) Give the intervals for which the function is constant, where it is increasing, and where it is decreasing. (Enter your answers using interval notation. constant [-7, 1] increasing [3, 5] decreasing [1, 3] U [5, 7]

Solution

If the gradient (first derivative) of the function changes sign at the stationary point, then it is called a turning point, which can be a local maximum or local minimum.

from the graph we can see that there are only two points where the function is changing from increasing to decreasing and vice versa.

Hence x-coordinates of turning points are 3,5