One of these I know is wrong ,one of these I don't understand how to do.
1) Use logarithmic differentiation to find the derivative of the function.
ln(y) = ln(x)ln(sin(x))
F(x) = ln(x)ln(sin(x))
f(x) = ln(x); f'(x) = 1/x
g(x) = ln(sin(x))
g'(x) = cosx/sinx
y'/y = [ln(sin(x))/x] + [ln(x)cos(x)/sin(x)]
y' = y{[ln(sin(x))/x] + [ln(x)cos(x)/sin(x)]}
y' = [sin(x)^ln(x)ln(sin(x))/x] + (ln(x)^2) * cos(x)
Not sure where i went wrong on that one.
2) The curve with equation y2 = x3 + 3x2 is called the Tschirnhausen cubic. -Find an equation of the tangent line to this curve at the point (1, -2).
-Find the points on the curve where the tangent line has a vertical asymptote
I was under the impression I had to derive the function, and then find points where it is undefined, but the question is asking for y, not y'.
#2 is wrong.
Thanks for the help so far, though.
Edit: And I was wrong, the question should read "The curve with equation y2 = x3 + 3x2 is called the Tschirnhausen cubic. Find an equation of the tangent line to this curve at the point (1, -2)
At what points does this curve have a horizontal tangent?"
However both parts were still maked incorrect, and the points are supposed to have different y values.
first, note how to denote exponents in your posts by looking at the correction above.
the derivative is the same as completed above.
substitute the given coordinates (1,-2) into the derivative to determine the slope of the tangent line ... then use the point-slope form of a linear equation to find the tangent line equation.
a horizontal tangent line occurs where = 0
set the derivative equal to 0, solve for x in terms of y or y in terms of x (whichever is easier), and substitute the result into the original equation for the curve ... solve.
Sorry about the notation. Was copy and pasting.
y = (-9/4x) -1/4
Solving dy/dx for x gave me -2 (marked correct) and 0 instead of -3 and 0.
Which gave me the points:
(0,-1/4)
(-2,17/4)
Am I mistaken? Still is getting refused (except for the -2)
Edit: Nevermind, I lost a sign. I got (-9/4)x + (1/4)
But the only coordinate that isn't being marked off is -2. -2 in that equation gives 19/4, correct? It's also still refusing to accept 0 as a valid point.
Edi2: I don't think I'm using the right equation. It doesn't look like subbing the x values into y' gives the proper number. Should the number be substituted into the original equation?