Question

Find the function $f$ given that the slope of the tangent line to the graph of $f$ at any point $(x, f(x))$ is $f^{\prime}(x)$ and that the graph of $f$ passes through the given point. $$f^{\prime}(x)=\frac{1}{2} x^{-1 / 2} ;(2, \sqrt{2})$$ 60. $$f^{\prime}(t)=t^{2}-2 t+3 ;(1,2)$$

Name: Problem 59, Chapter 11: Applied Mathematics: For the Managerial, Life, and Social Sciences
Uploaded: 2021-05-10T15:08:37-08:00
Duration: 3 min 9 s
Channel: Gregory Higby
Description: Find the function f given that the slope of the tangent line to the graph of f at any point (x, f(x)) is f^'(x) and that the graph of f passes through the given point. f^'(x)=(1)/(2) x^-1 / 2 ;(2, √(2)) 60. f^'(t)=t^2-2 t+3 ;(1,2)

   Find the function $f$ given that the slope of the tangent line to the graph of $f$ at any point $(x, f(x))$ is $f^{\prime}(x)$ and that the graph of $f$ passes through the given point.
$$f^{\prime}(x)=\frac{1}{2} x^{-1 / 2} ;(2, \sqrt{2})$$
60. $$f^{\prime}(t)=t^{2}-2 t+3 ;(1,2)$$

Applied Mathematics: For the Managerial, Life, and Social Sciences

Soo T. Tan 5th Edition

Chapter 11, Problem 59

Instant Answer

Solved by Expert Gregory Higby

05/10/2021

Step 1

This means that the derivative of $f$ is equal to $f^{\prime}(x)$. So we have $f'(x) = \frac{1}{2}x^{-1/2}$. Show more…

Show all steps

Thanks for your feedback!

Find the function $f$ given that the slope of the tangent line to the graph of $f$ at any point $(x, f(x))$ is $f^{\prime}(x)$ and that the graph of $f$ passes through the given point. $$f^{\prime}(x)=\frac{1}{2} x^{-1 / 2} ;(2, \sqrt{2})$$ 60. $$f^{\prime}(t)=t^{2}-2 t+3 ;(1,2)$$

Play audio

Feedback

Gregory Higby and 81 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Initial Condition

An initial condition is a specified value of the function at a particular point. It is used to determine the constant of integration from the antiderivative, thereby identifying a unique solution among the infinite family of functions that differ by a constant.

Derivative as Slope

The derivative of a function represents the slope of the tangent line to the function's graph at any point. This concept is crucial for understanding how the function changes at a point and is fundamental to many topics in calculus.

Antiderivative

The antiderivative of a function is a function whose derivative is the given function. It is used to reverse the process of differentiation and is essential when solving problems that require finding the original function from its derivative.

Please give Ace some feedback