How do you find the slope of the secant lines of f(x)=x through the points: [3, 5]?

Expert answers to "How do you find the slope of the..."

High School
Calculus and Analysis
Calculus 1
Derivatives

Beckham Short

Answered question

2022-04-09

How do you find the slope of the secant lines of

f (x) = \sqrt{x}

through the points: [3, 5]?

Answer & Explanation

annie996k88v

Beginner2022-04-10Added 11 answers

Explanation:
We have two points: one that passes through the point on the function at x=3, and the other which passes through the function at x=5.
The slope of the line is found through

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

. Here, our x values are 3 and 5, and our y values are the function values for these.
The y value for x=3 is

f (3) = \sqrt{3}

. For x=5, the y value is

f (5) = \sqrt{5}

.
Thus, the secant line's slope is

\frac{\sqrt{5} - \sqrt{3}}{5 - 3} = \frac{\sqrt{5} - \sqrt{3}}{2} \approx 0.2520

We can formalize this all by saying that the slope of secant line passing through
x=a and x=b is equal to

\frac{f (b) - f (a)}{b - a}

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?