Find $f$. $f'(x) = \frac{(x+1)}{\sqrt{x}}$, $f(1) = 4$ $f(x) = \boxed{}$
Added by Kevin O.
Close
Step 1
The given derivative is $f'(x) = \frac{x+1}{\sqrt{x}}$. To find $f(x)$, we need to integrate $f'(x)$ with respect to $x$. First, simplify the expression for $f'(x)$: $f'(x) = \frac{x}{\sqrt{x}} + \frac{1}{\sqrt{x}}$ $f'(x) = x^{1 - 1/2} + x^{-1/2}$ $f'(x) = Show more…
Show all steps
Your feedback will help us improve your experience
Amit Srivastava and 57 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Particular antiderivatives For the following functions $f,$ find the antiderivative $F$ that satisfies the given condition. $$f(x)=(4 \sqrt{x}+6 / \sqrt{x}) / x^{2} ; F(1)=4$$
Applications of the Derivative
Antiderivatives
For the following functions $f$, find the anti-derivative $F$ that satisfies the given condition. $$f(x)=4 \sqrt{x}+6 ; F(1)=8$$
Find $ f $. $ f'(x) = 1 + 3\sqrt{x} $, $ \quad f(4) = 25 $
Applications of Differentiation
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD