# What are the critical points of # f(x,y)=sin(x)cos(y) +e^xtan(y)#?

When

A graph of solutions is here

By signing up, you agree to our Terms of Service and Privacy Policy

To find the critical points of the function ( f(x, y) = \sin(x)\cos(y) + e^x\tan(y) ), we need to find where the partial derivatives with respect to ( x ) and ( y ) are both zero.

The partial derivatives of ( f(x, y) ) with respect to ( x ) and ( y ) are as follows:

[ \frac{\partial f}{\partial x} = \cos(x)\cos(y) + e^x\tan(y) ] [ \frac{\partial f}{\partial y} = -\sin(x)\sin(y) + e^x\sec^2(y) ]

Setting these derivatives equal to zero and solving for ( x ) and ( y ) will give us the critical points. However, finding explicit solutions for this system of equations might be challenging, and numerical methods may be needed.

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.

- Is #f(x)=(x^2-e^x)/(x-2)# increasing or decreasing at #x=-1#?
- How do you find the local extrema for #f(x) = 2-2x^2# on domain #-1 <= x <= 1#?
- How do you find the local max and min for #f (x) = x^(3) - 6x^(2) + 5#?
- How do you find the critical numbers of #y= 2x-tanx#?
- Is #f(x)=1/x-1/x^3+1/x^5# increasing or decreasing at #x=2#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7