Blog
Algebra

Y=sin(x^(1.7/6)+4)+(1/x))+10

Input y = sin(x^(1.7/6) + 4) + 1/x + 10 Result y = sin(x^0.283333 + 4) + 1/x + 10 Property as a real function {x element R : x>0} (all positive real numbers)

Read More
Algebra

Y=sin(3x)

Input y = sin(3 x) Roots x = (pi n)/3, n element Z Derivative (d)/(dx)(sin(3 x)) = 3 cos(3 x) Global maxima max{sin(3 x)} = 1 at x = (2 pi n)/3 + pi/6 for integer n

Read More
Algebra

Y=mx+b solve for b

Input interpretation solve y = m x + b for b Result b = y – m x

Read More
Algebra

Y=f(-x)

Input y = f(-x) Derivative (d)/(dx)(f(-x)) = -f'(-x)

Read More
Algebra

Y=ax^2

Input y = a x^2 Geometric figure parabola Alternate form y – a x^2 = 0 Derivative (d)/(dx)(a x^2) = 2 a x

Read More
Algebra

Y=absolute value of x

Input y = abs(x) Alternate form assuming x and y are positive x = y Alternate form assuming x and y are real y = sqrt(x^2) Root x = 0 Derivative (d)/(dx)(abs(x)) = x/(abs(x)) Global minimum min{abs(x)} = 0 at x = 0

Read More
Algebra

Y=a(x-h)^2+k

Input y = a(x – h)^2 + k Property as a real function R (all real numbers) Derivative (d)/(dx)(a(x – h)^2 + k) = 2 a(x – h) a'(x – h)

Read More
Algebra

Y=9+3z

Input y = 9 + 3 z Geometric figure line Root z = -3

Read More
Algebra

Y=9/x

Input y = 9/x Geometric figure hyperbola Alternate form assuming x and y are positive x y = 9 Roots (no roots exist) Derivative (d)/(dx)(9/x) = -9/x^2 Limit lim_(x-> ± infinity) 9/x = 0

Read More
Algebra

Y=8x^3

Input y = 8 x^3 Alternate form y – 8 x^3 = 0 Root x = 0 Derivative (d)/(dx)(8 x^3) = 24 x^2

Read More