do you know how to differentiate implicitly? you can do that and solve for y'. you can use that to find the slope. then the equation of the tangent line is given by , just solve for y. Here, is the slope, given by the derivative that you found earlier, is a point the line passes through. it will be you can solve for using the initial equation, you'll need to do this anyway to get the slope.

find and .Given the function f(x)=ln(3+sinx) on the interval [0,7]

a. at which values of x does f have local max and local min

To find the critical points, set and solve for (only take the values between 0 and 7 inclusive.

To find whether the point you found above are max's or min's, check the following:

If then we have a local max

If then we have a local min