I am to find the number of points (by hand ) where the curve x^2 - xy + (3/4)y^2 = 7 has horizontal tangent lines.
what i did was i took the derivative:
2x-y+(3/2)y = 0
simplified:
2x - (1/2) y = 0
solved for y:
2x = (1/2)y
4x = y
plugged it into the original to find my x value
x=+/- sqrt(7)/3
what do i do from here?
As usual, straight continuous lines differentiate (downward) with respect to x, straight dashed lines with respect to the dashed balloon expression. So the left triangular network is a 'product-rule shape' and the other one a 'chain-rule shape'.
Don't integrate - balloontegrate! Balloon Calculus: worked examples from past papers