Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Given f^ prime prime (x)=x+2 and f^ prime (0)=3 and f(0) = - 1. Find f(x).

Given F Prime Prime Xx2 And F Prime 03 And F0 1 Find Fx class=

Sagot :

Given

The derivative function is given as

[tex]f^{\prime}^{\prime}(x)=x+2[/tex]

and f(0) = - 1 and f'(0) = 3

Explanation

To determine the function,

[tex]\begin{gathered} \int d^2y=\int(x+2)dx^2 \\ \frac{dy}{dx}=\frac{x}{2}^2+2x+C \\ f^{\prime}(0)=\frac{0}{2}^2+2(0)+C \\ 3=C \end{gathered}[/tex]

It is also given that f(0) = - 1.

[tex]f^{\prime}(x)=\frac{x^2}{2}+2x+3[/tex]

Take the integral and find the function

[tex]\begin{gathered} \int dy=\int\frac{x^2}{2}+2x+3dx \\ y=\frac{x^3}{6}+\frac{2x^2}{2}+3x+C \\ y=\frac{x^3}{6}+x^2+3x+C \\ f(x)=\frac{x^3}{6}+x^2+3x+C \\ -1=0+C \\ C=-1 \end{gathered}[/tex]

Then the function is determined as

[tex]y=\frac{x^3}{6}+x^2+3x-1[/tex]

Answer

Hence the function is determined as

[tex]f(x)=\frac{x^3}{6}+x^2+3x-1[/tex]

Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.