Z=9-y^2
Input z = 9 – y^2 Geometric figure parabola Derivative (d)/(dy)(9 – y^2) = -2 y Global maximum max{9 – y^2} = 9 at y = 0
Z^2 = x^2 + y^2
Input z^2 = x^2 + y^2 Geometric figure infinite cone Alternate form -x^2 – y^2 + z^2 = 0
Z=1+x+y
Input z = 1 + x + y Geometric figure plane Alternate form -x – y + z – 1 = 0 Real root y = -x – 1 Root y = -x – 1 Derivative (d)/(dx)(1 + x + y) = 1
Y2 = x2 + 2z2
Input y^2 = x^2 + 2 z^2 Geometric figure infinite elliptic cone
Y-y1=m(x-x1)
Input y – y1 = m(x – x1) Solution y1 = y – m(x – x1) Solution for the variable y y = m(x – x1) + y1
Y=-x-3
Input y = -x – 3 Geometric figure line Alternate form x + y + 3 = 0 Root x = -3 Derivative (d)/(dx)(-x – 3) = -1
Y=x3
Input y = x^3 Alternate form y – x^3 = 0 Root x = 0 Derivative (d)/(dx)(x^3) = 3 x^2
Y=x+4 slope
Input interpretation plane curve | Cartesian equation y = x + 4 | slope Result 1 Geometric figure line Properties of line x-intercept | -4 y-intercept | 4 slope | 1
Y=sqrt(x+4)
Input y = sqrt(x + 4) Geometric figure parabola Root x = -4 Derivative (d)/(dx)(sqrt(x + 4)) = 1/(2 sqrt(x + 4)) Global minimum min{sqrt(x + 4)} = 0 at x = -4
Y=sin2x
Input y = sin(2 x) Roots x = (pi n)/2, n element Z Derivative (d)/(dx)(sin(2 x)) = 2 cos(2 x) Global maxima max{sin(2 x)} = 1 at x = pi n + pi/4 for integer n