Resolved: "How do you differentiate f(x)=3?"

High School
Calculus and Analysis
Calculus 1
Derivatives

Jasiah Vincent

Answered question

2022-04-17

How do you differentiate f(x)=3?

Answer & Explanation

Egerlandsq0z

Beginner2022-04-18Added 14 answers

Using the definition?
there's nothing very special about 3 here.
f(x)=c Note this makes f(x+h)=c as well.

f^{'} (x) = lim_{h \to 0} \frac{f (x + h) - f (x)}{h}

= lim_{h \to 0} \frac{c - c}{h} = lim_{h \to 0} \frac{0}{h}

For

h \neq 0

, we have

\frac{0}{h} = 0

so, we continue:

= lim_{h \to 0} 0 = 0

That is: for f(x)=c, we have f'(x)=0.
Note that this makes sense geometrically too. We "get at" the slope of the tangent line by looking at slopes of secant line to the graph and then finding a limit.
For any two points on the graph of f(x)=3, we have slope m=0 Taking a limit wont't change this slope. (Next exercise, think about the slope of any line y=mx+b).

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Calculus 1

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function
$f (x, y) = x^{3} - 6 x y + 8 y^{3}$
$\frac{1}{\sec (x)}$ in derivative?
What is the derivative of $\ln (x + 1)$ ?
What is the limit of $e^{- x}$ as $x \to \infty$ ?
What is the derivative of $f (x) = 5^{\ln x}$ ?
What is the derivative of $e^{- 2 x}$ ?
How to find $lim \frac{e^{t} - 1}{t}$ as $t \to 0$ using l'Hospital's Rule?
What is the integral of $\sqrt{9 - x^{2}}$ ?
What is the derivative of $f (x) = \ln [x^{9} {(x + 3)}^{6} {(x^{2} + 7)}^{5}]$ ?
What Is the common difference or common ratio of the sequence 2, 5, 8, 11...?
How to find the derivative of $y = e^{5 x}$ ?
How to evaluate the limit $\frac{\sin (5 x)}{x}$ as x approaches 0?
How to find derivatives of parametric functions?
What is the antiderivative of $- 5 e^{x - 1}$ ?
How to evaluate: indefinite integral $\frac{1 + x}{1 + x^{2}} d x$ ?

Didn't find what you were looking for?