differentiation

Consider a function f(x,y,z) given by f(x, y, z) = (x² + y² - 2z²) (y² + z²) The partial derivative of this function with respect to x at the point,x = 2, y = 1 and z = 3 is

Minimum of the real valued function $$f\left( x \right) = {\left( {x - 1} \right)^{2/3}}$$ occurs at $$x$$ equal to

The minimum value of the function $$f\left( x \right) = {x^3} - 3{x^2} - 24x + 100$$ in the interval $$\left[ { - 3,3} \right]$$ is

Let $$f\left( x \right) = x{e^{ - x}}.$$ The maximum value of the function in the interval $$\left( {0,\infty } \right)$$ is

A function $$y = 5{x^2} + 10x\,\,$$ is defined over an open interval $$x=(1,2).$$ At least at one point in this interval, $${{dy} \over {dx}}$$ is exactly

The maximum value of $$f\left( x \right) = {x^3} - 9{x^2} + 24x + 5$$ in the interval $$\left[ {1,6} \right]$$ is

The function $$f\left( x \right) = 2x - {x^2} + 3\,\,$$ has

Consider the function $$f\left( x \right) = {\left( {{x^2} - 4} \right)^2}$$ where $$x$$ is a real number. Then the function has

For the function $$f\left( x \right) = {x^2}{e^{ - x}},$$ the maximum occurs when $$x$$ is equal to