Question
Find a function $f$ such that $f^{\prime \prime}(x)=6, f^{\prime}(-1)=2,$ and $f(-1)=0$
Step 1
To find the first derivative $f^{\prime}(x)$, we need to integrate $f^{\prime \prime}(x)$ with respect to $x$. \[f^{\prime}(x) = \int f^{\prime \prime}(x) dx = \int 6 dx = 6x + C\] Show more…
Show all steps
Your feedback will help us improve your experience
Gregory Higby and 79 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
Find a function $f$ such that $f(1)=0$ and $f^{\prime}(x)=2^{\prime} / x$
Integrals
The Fundamental Theorem of Calculus
$$\begin{array}{l}{\text { Find the function } f \text { such that } f^{\prime}(x)=f(x)(1-f(x)) \text { and }} \\ {f(0)=\frac{1}{2} .}\end{array}$$
Differential Equations
Separable Equations
Find the function $f$ such that $f^{\prime}(x)=f(x)(1-f(x))$ and $f(0)=\frac{1}{2} .$
APPLICATIONS OF INTEGRATION
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD