Question

A curve is concave up if (d^2 y)/ [dx] ^2 is

negative

positive

zero

None of these​

Answer 1

Answer:

zero is the correct answer

Step-by-step explanation:

please mark as brainleist answer

Answer 2

Answer:

can eliminate the parameter by first solving the equation x(t)=2t+3 for t:

x(t)x−3t===2t+32tx−32.

Substituting this into y(t), we obtain

y(t)yyy====3t−43(x−32)−43x2−92−43x2−172.

The slope of this line is given by dydx=32. Next we calculate x′(t) and y′(t). This gives x′(t)=2 and y′(t)=3. Notice that dydx=dy/dtdx/dt=32. This is no coincidence, as outlined in the following theorem.

THEOREM 1.1

Derivative of Parametric Equations

Consider the plane curve defined by the parametric equations x=x(t) and y=y(t). Suppose that x′(t) and y′(t) exist, and assume that x′(t)≠0. Then the derivative dydx is given by

dydx=dy/dtdx/dt=y′(t)x′(t).

1.1