Problem

The graph of a function is shown in the figure. M…

01:11

Problem 52 Easy Difficulty

The graph of a function $ f $ is shown. Which graph is an antiderivative of $ f $ and why?

Name: the graph of a function f is shown which graph is an antiderivative of f and why 2
Uploaded: 2021-02-11
Duration: 2 min 46 s
Channel: Numerade
Description: The graph of a function $ f $ is shown. Which graph is an antiderivative of $ f $ and why?

Answer

This condition is satisfied the curve $a$ -The black curve.

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Video Transcript

Okay. I have a picture of f here, and I want to find the anti derivative of F. Okay, well, just draw one, and then you can pick which one is it in the exercise. Okay, so if we're trying to draw the anti derivative of F, then that means we're looking for the function that f is the derivative of So f is the derivative of some function G. So G is the anti derivative really? Of f you okay, So f is the derivative. Okay, so where the derivative is zero right here. That means G has a max or men right here. Okay. Here from here. Thio here. The derivative is positive. Okay. F is positive here because it's above the X axis. That means G is increasing. F is positive, So g is increasing. And then here f is negative. Sergey decreasing. Okay, that might be enough. So let's have a look. So it was a start somewhere. And when we get to this point, we're going to stop increasing and we're going to start decreasing. Okay, so we're gonna increase till we get to some point right here, and then that will be the Max and then we're going to decrease like that. How much? I don't know. That's good enough. So what you have to do now is look at the pictures and find one that has this general shape. And if you notice, it will be a the black drawing because it increases reaches a maximum and then it decreases.

Linda H.

Oklahoma State University

Topics

Derivatives

Differentiation

Volume

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives