(-6, 2) (3, 2) y 1 O 1 x Graph of f' 3. The function f is...

(-6, 2) (3, 2) y 1 O 1 x Graph of f' 3. The function f is differentiable on the closed interval [-6, 5] and satisfies f(-2) = 7. The graph of f', the derivative of f, consists of a semicircle and three line segments, as shown in the figure above. (a) Find the values of f(-6) and f(5). (b) On what intervals is f increasing? Justify your answer. (c) Find the absolute minimum value of f on the closed interval [-6, 5]. Justify your answer. (d) For each of f"(-5) and f"(3), find the value or explain why it does not exist.

Transcript

00:01 Hello students.

00:02 Here we have the graph of f dash of x that is the first relative.

00:06 So this function is differentiable in minus 6 .5 and we have f of minus 2a7.

00:11 So we have to find f of minus 6 and f of 5 and we have to find out on what interval is increasing.

00:18 We have to find the absolute minimum value of f and we have to find f double dash of minus 5 and f double dash of 3.

00:26 So let me start.

00:28 First of all, we can just draw another graph now we can go the increasing decrease in graph so here the f of x is here is minus 6 to 2 so we can simply draw that from minus 6 to 2 okay so here the function is increasing correct now what is happening here we have this curve because semicircle from minus 2 to 2.

01:07 Okay, so it goes to minus 2.

01:10 So the corresponding graph will be here.

01:16 So the minus 2.

01:19 Now, from it, it's increasing, increasing, decreasing graph.

01:28 Increasing, decreasing.

01:37 Okay.

01:39 So now we can find answers v.

01:41 What is the question number a? question where we get to find f of minus six from the figure f of minus six will be zero now we have to find out f of five f of five will be having the value two now what about the second one in the b part in there also on the function of increasing the function is increasing from increasing from minus six to minus two and also it is increased from 2 to 5 correct 2 to 5 okay this data we can obtain easily obtain from the graph okay so a function is increasing what is the reason for that a function is increasing function is increasing when f dash of x is greater than 0 okay if that ft of x is greater than 0 okay if that's of x is greater than 0.

02:52 So we can just throw the graph...

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