How do you find the maximum and minimum values of the function #f(x)= x - ((64x)/(x+4))# on the interval [0,13]?
There is only a local minimum at
The derivative of
And by the quotient rule
Therefore,
The critical points are when
graph{x-((64x)/(x+4)) [-73.8, 113.7, -63, 30.8]}
By signing up, you agree to our Terms of Service and Privacy Policy
To find the maximum and minimum values of the function ( f(x) = x - \frac{64x}{x+4} ) on the interval ([0,13]), follow these steps:
-
Find the critical points of the function within the given interval by setting its derivative equal to zero and solving for ( x ).
-
Evaluate the function at the critical points as well as at the endpoints of the interval ([0,13]).
-
The maximum and minimum values will be the maximum and minimum function values obtained from the critical points and endpoints.
-
Check for critical points that lie outside the interval, as they won't be considered in this case.
After evaluating the function, you can determine the maximum and minimum values within the given interval.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- What are the extrema of #g(x) = 5x-80?# on the interval #[-1,10]#?
- What is the minimum value of #g(x) = x^2-2x - 11/x?# on the interval #[1,7]#?
- How do you find the values of C guaranteed by the Mean Value Theorem for #f(x)= 9/x^3# over [1, 3]?
- Is #f(x)=x^2lnx# increasing or decreasing at #x=1#?
- What are the extrema and saddle points of #f(x, y) = xy(1-x-y)#?
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7