this is section 3.3 problem 8: the function y = h(x) is represented by the graph in the textbook. use the…

this is section 3.3 problem 8: the function y = h(x) is represented by the graph in the textbook. use the graph to find intervals and x - values that satisfy the following conditions. the answers should be in ascending order and either be an integer or an integer and a half such as \1.5\. use \dne\ if such interval does not exist. (a) the intervals on which the derivative is positive are ( , ) and ( , ). (b) the intervals on which the derivative is negative are ( , ) and ( , ). (c) the x - values at which the derivative equals zero are x = and . (d) the x - values at which the derivative does not exist are x = and . hint: refer to theorem 1. resources ebook submit answer details my notes previous answers ask your teacher 8. y = h(x) 9. for the function graphed in 1 determine (a) the point(s) at which h has a maximum; (b) the point(s) at which h has a minimum;

this is section 3.3 problem 8: the function y = h(x) is represented by the graph in the textbook. use the graph to find intervals and x - values that satisfy the following conditions. the answers should be in ascending order and either be an integer or an integer and a half such as \1.5\. use \dne\ if such interval does not exist. (a) the intervals on which the derivative is positive are ( , ) and ( , ). (b) the intervals on which the derivative is negative are ( , ) and ( , ). (c) the x - values at which the derivative equals zero are x = and . (d) the x - values at which the derivative does not exist are x = and . hint: refer to theorem 1. resources ebook submit answer details my notes previous answers ask your teacher 8. y = h(x) 9. for the function graphed in 1 determine (a) the point(s) at which h has a maximum; (b) the point(s) at which h has a minimum;

Answer

Explanation:

Step1: Analyze positive - derivative intervals

When the derivative of a function (y = h(x)) is positive, the function is increasing. By observing the graph, we can see that the function is increasing on the intervals ((-3, - 2)) and ((1,2)).

Step2: Analyze negative - derivative intervals

When the derivative of a function (y = h(x)) is negative, the function is decreasing. By observing the graph, we can see that the function is decreasing on the intervals ((-2,1)) and ((2,4)).

Step3: Find where derivative is zero

The derivative of a function is zero at the points where the slope of the tangent line to the graph is zero. From the graph, the derivative is zero at (x = 2) and (x=-3).

Step4: Find where derivative does not exist

The derivative does not exist at the points where there are sharp - corners or vertical tangents. From the graph, there are no such points indicated.

Answer:

(a) The intervals on which the derivative is positive are ((-3,-2)) and ((1,2)). (b) The intervals on which the derivative is negative are ((-2,1)) and ((2,4)). (c) The (x) values at which the derivative equals zero are (x=-3) and (x = 2). (d) The (x) values at which the derivative does not exist: DNE.