# The special case of x⁴

The special case of x⁴ holds a unique significance in mathematics, representing a prominent polynomial expression characterized by its quartic power. Its distinct properties and behaviors contribute to various mathematical disciplines, including algebra, calculus, and geometry. Examining x⁴ allows for deeper insights into polynomial functions, symmetry, and root analysis. In both theoretical and practical contexts, understanding the intricacies of this specific case provides a foundation for tackling more complex mathematical problems and applications.

Questions

- How do you find the antiderivative of #x^2+5x#, if the point (0,5) exists on the graph of the antiderivative?
- How do you find the stationary points for #f(x)=x^4# ?
- What can you say about the graph of a solution of the equation y' = #(xy^3)/36# when x is close to 0?
- Let y = [f(x)]3 and suppose that f′ (1) = 4 and y′ = 10 for x = 1. Find f(1)?
- Find the derivative using logarithmic differentiation?
- What is the general solution of the differential equation #dy/dx+x^4y=3x^4 (x>0)#? Express the answer in explicit form.
- If #f(x) = x^2-4# and #g# is a differentiable function of #x#, what is the derivative of #f(g(x))#?
- How do you find the relative extrema for #f(x)=x^4# ?
- The area of the region bounded by the curve y=x^2 and y=4x-x^2 is ?
- What is the inverse function of #f(x)=1/(1+x)#. How inverse functions appear in graph?
- Trace the curve x[y^(2)+4]=8 stating all the points used for doing so?
- What the area of the figure bounded by the given curve y=(x*(sqrt36-x^2)) (0_< x_< 6)?
- How do you determine the concavity for #f(x)=x^4# ?
- How do you find the inflection points for #f(x)=x^4# ?
- Determine the forth derivative of this function f(x)=x^4+3x^2-2/√x?
- How do you solve it ? (x−4)*y′=5*y+3
- Find y' and y''? #y = x^2ln(2x)#
- How to investigate the following function and plot its graphs using the methods of differential calculus? y=3x-2 / x^2
- Solve the differential equation #y'=(y-x)^2#?
- How do you find a definite integral that represents the arc length of the curve over the indicated interval #y=x^2+x+4# for #0lexle2# ?