Question

Find all functions \( g \) such that \[ g^{\prime}(x)=\frac{4 x^{2}+x+3}{\sqrt{x}} . \] 1. \( g(x)=2 \sqrt{x}\left(4 x^{2}+x-3\right)+C \) 2. \( g(x)=2 \sqrt{x}\left(\frac{4}{5} x^{2}+\frac{1}{3} x-3\right)+C \) 3. \( g(x)=\sqrt{x}\left(4 x^{2}+x+3\right)+C \) 4. \( g(x)=\sqrt{x}\left(\frac{4}{5} x^{2}+\frac{1}{3} x+3\right)+C \) 5. \( g(x)=2 \sqrt{x}\left(4 x^{2}+x+3\right)+C \) 6. \( g(x)=2 \sqrt{x}\left(\frac{4}{5} x^{2}+\frac{1}{3} x+3\right)+C \) correct

          Find all functions \( g \) such that
\[
g^{\prime}(x)=\frac{4 x^{2}+x+3}{\sqrt{x}} .
\]
1. \( g(x)=2 \sqrt{x}\left(4 x^{2}+x-3\right)+C \)
2. \( g(x)=2 \sqrt{x}\left(\frac{4}{5} x^{2}+\frac{1}{3} x-3\right)+C \)
3. \( g(x)=\sqrt{x}\left(4 x^{2}+x+3\right)+C \)
4. \( g(x)=\sqrt{x}\left(\frac{4}{5} x^{2}+\frac{1}{3} x+3\right)+C \)
5. \( g(x)=2 \sqrt{x}\left(4 x^{2}+x+3\right)+C \)
6. \( g(x)=2 \sqrt{x}\left(\frac{4}{5} x^{2}+\frac{1}{3} x+3\right)+C \) correct

Find all functions g such that

g^'(x)=(4 x^2+x+3)/(√(x)) .

1. g(x)=2 √(x)(4 x^2+x-3)+C
2. g(x)=2 √(x)((4)/(5) x^2+(1)/(3) x-3)+C
3. g(x)=√(x)(4 x^2+x+3)+C
4. g(x)=√(x)((4)/(5) x^2+(1)/(3) x+3)+C
5. g(x)=2 √(x)(4 x^2+x+3)+C
6. g(x)=2 √(x)((4)/(5) x^2+(1)/(3) x+3)+C correct

Added by Joel W.

Calculus: Early Transcendental Functions

Robert T. Smith, Roland B. Minton 3rd Edition

Chapter 2

Instant Answer

Solved by Expert Vishal Parmar

Step 1

We need to find the function \( g(x) \) such that its derivative \( g'(x) = \frac{4x^2 + x + 3}{\sqrt{x}} \). Show more…

Show all steps

Thanks for your feedback!

Find all functions \( g \) such that \[ g^{\prime}(x)=\frac{4 x^{2}+x+3}{\sqrt{x}} . \] 1. \( g(x)=2 \sqrt{x}\left(4 x^{2}+x-3\right)+C \) 2. \( g(x)=2 \sqrt{x}\left(\frac{4}{5} x^{2}+\frac{1}{3} x-3\right)+C \) 3. \( g(x)=\sqrt{x}\left(4 x^{2}+x+3\right)+C \) 4. \( g(x)=\sqrt{x}\left(\frac{4}{5} x^{2}+\frac{1}{3} x+3\right)+C \) 5. \( g(x)=2 \sqrt{x}\left(4 x^{2}+x+3\right)+C \) 6. \( g(x)=2 \sqrt{x}\left(\frac{4}{5} x^{2}+\frac{1}{3} x+3\right)+C \) correct