Compute f'(3), where f(x)=x2−8x.

Step 1For a function f(x) its derivative is given by the definition limh→0f(x+h)−f(x)h. For some standard functions like xn the derivative is known so there is no need to find derivative of functions written in terms of standard functions.Use one property of derivatives (f(x)+g(x))′=f'(x)+g'(x). Use another property of derivatives (cf(x))′=cf'(x). Use the derivative of xn,n≠q0 is equal to nxn−1.Step 2Given function is f(x)=x2−8x. Find its first derivative and then substitute x=3 to find f'(3).f(x)=x2−8xf′(x)=(x2−8x)′=(x2)′−(8x)′=2x-8(x)'=2x-8f'(3)=2*3-8=-2Hence, for the given function f'(3)=−2.

Explained: "Compute f'(3), where f(x)=x2−8x."

High School
Calculus and Analysis
Calculus 1
Derivatives

Yulia

Answered question

2021-05-19

Compute f'(3), where

f (x) = x^{2} - 8 x

Answer & Explanation

Nathalie Redfern

Skilled2021-05-20Added 99 answers

Step 1
For a function f(x) its derivative is given by the definition

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

. For some standard functions like

x^{n}

the derivative is known so there is no need to find derivative of functions written in terms of standard functions.
Use one property of derivatives (f(x)+g(x))′=f'(x)+g'(x). Use another property of derivatives (cf(x))′=cf'(x). Use the derivative of

x^{n}, n \neq q 0

is equal to

n x^{n - 1}

.
Step 2
Given function is

f (x) = x^{2} - 8 x

. Find its first derivative and then substitute x=3 to find f'(3).

f (x) = x^{2} - 8 x

f^{'} (x) = {(x^{2} - 8 x)}^{'}

= {(x^{2})}^{'} - {(8 x)}^{'}

=2x-8(x)'
=2x-8
f'(3)=2*3-8
=-2
Hence, for the given function f'(3)=−2.

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?