💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Like

Report

If $ f'(x) = c $ ($ c $ a constant) for all $ x $, use Corollary 7 to show that $ f(x) = cx + d $ for some constant $ d $.

See proof

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 2

The Mean Value Theorem

Derivatives

Differentiation

Volume

Missouri State University

University of Nottingham

Boston College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

01:29

Constant Rule proof For th…

01:51

Find $f^{\prime}(x)$

01:01

Use the Product Rule to sh…

01:33

05:05

a) Show that if $f(x)$ and…

01:27

Let $f(x)=a x+b$ and $g(x)…

00:22

Show that, for any constan…

0:00

For what value of the cons…

00:56

02:51

Let $ f(x) = 1/x $ and…

Okay, um we're being told that if f prime of X is equal to see and she is a constant for all X used Kerala very seven to show that f of X equals cfx. I mean, see explosive t with them constantly. So here, um in case you do not know what the Kerala very seven is and the Stuart textbook, I've restated it right here, and I'm going to stay there. So if f prime of X equals g prime back for all X and a B, then f of X equals G of X plus D for some constant d. So that is a statement. So we have to make a couple of assumptions. So we're told that F Prime of X is equal to see And in order to proceed with this, we're going to also create a function called G of X. So, So g of X, Um, we're gonna say it equals cfx so that when we take the derivative of G primary rex, it will equal See now, since primary, Rex and G Prime of X is equal to each other in this case, that and that's just a little case we made up. Um, we can actually apply Kerala very seven right away. Because corroborate 77 f prime lexical G prime of X. We can apply the statement f of X equals G of exports D So we can now. Now we can now use that formula f of X equals she of X Oh, dear. And since we have G FX, we can substitute that. You say after Becks is equal to see X plus d. Come on. And that is what we were asked. That's what we were being asked to prove so that of alphabetical cfx for the using corollary seven Oh!

Numerade Educator

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

Constant Rule proof For the constant function $f(x)=c,$ use the definition o…

$$f(x)=a x^{3}+b x^{2}+c x+d \quad(a, b, c,…

Use the Product Rule to show that$\frac{d}{d x}(c \cdot f(x))=c \cdot \f…

$$f(x)=\frac{1}{a}\left(x^{2}+\frac{1}{b} x…

a) Show that if $f(x)$ and $g(x)$ are functions such that $f(x)$ is $o(g(x))…

Let $f(x)=a x+b$ and $g(x)=c x+d,$ where $a, b, c,$ and $d$ are constants. D…

Show that, for any constant $k$$$\frac{d}{d x}\left[\frac{f(x)}{k}\r…

For what value of the constant $ c $ is the function $ f $ continuous on $ (…

Show that, for any constant $k$

$\frac{d}{d x}\left[\frac{f(x)}{k}\r…

Let $ f(x) = 1/x $ and $$ g(x) = \left\{ \begin{array}…