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Unit circle: x² + y² = 1 when x = sqrt(3)/2:  y² = 1 - (sqrt(3)/2)²  y² = 1 - 3/4  y² = 1/4  y = 1/2 or -1/2 (first quadrant, so y is posi...

Set f(x)= (x^4)-14x. f’(x)=4(x^3)-14=2(2(x^3)-7). Thus we can write (2(x^3)-7)/((x^4)-14x)=(1/2)f’(x)/f(x). The integral of f’(x)/f(x)=ln|f(x)|+c. Thus the integral of (2(x^3)-7)/((x^4)-14x) is (1/2)(ln|f...

First differentiate: dx/dt = 3,   dy/dt = 3t² - 10t + 7

Using the chain rule: dy/dx = dy/dt * dt/dx = (3t² - 10t + 7)/3 

At stationary points, the...