MHB Differentiation / Integration Help

Joe20
Messages
53
Reaction score
1
The curve has a gradient function dy/dx = 2 +q/(5x^2) where q is a constant, and a turning point at (0.5, -4). Find the value of q.

option 1 : 2.5
option 2: -2.5
option 3: 0
Option 4: -3

I couldn't find the answer and will need assistance to how the answer can be obtained.

I have substituted x = 0.5 into dy/dx to get the gradient expression of 2 + 4q/5 and integrated to get y = 2x - q/(5x) + c.
It seems impossible for me to get the value of q since c could not be found. I am not sure if the question has some missing information to continue. Your help will be greatly appreciated. Thanks.
 
Physics news on Phys.org
Since the given point is a turning point, we must have:

$$\left.\d{y}{x}\right|_{x=\frac{1}{2}}=2+\frac{q}{5\left(\frac{1}{2}\right)^2}=2+\frac{4q}{5}=0$$

Now you just need to solve for $q$.
 
For original Zeta function, ζ(s)=1+1/2^s+1/3^s+1/4^s+... =1+e^(-slog2)+e^(-slog3)+e^(-slog4)+... , Re(s)>1 Riemann extended the Zeta function to the region where s≠1 using analytical extension. New Zeta function is in the form of contour integration, which appears simple but is actually more inconvenient to analyze than the original Zeta function. The original Zeta function already contains all the information about the distribution of prime numbers. So we only handle with original Zeta...
Back
Top