# The special case of x⁴ - Page 3

Questions

- Calculate the area between the curve y=3x-x^2 and the x axis between x=10 and x= 6?
- Consider the curve where a and b are constants. The normal to this curve at the point where x=4 is 4x+y=22. Find the values of a and b?
- With what integer a is the the graph #y=4x-2# the tangent line of #y=ax^2+28x+14#?
- Find the derivative of the inverse of the given function at the given point? f(x)=5x+#3x^2#+7x+2 at (13,1) help me please
- If 3x^2y+2x=-32 and dy/dt=-4 when x=2 and y=-3, how do you find dx/dt?
- What is the derivative of x^(10x)?
- Find the equation of the tangent line to the curve #y=x^4+2 e^x# at the point #(0,2)#.?
- Can I get help with this calculus problem? Let f(x)=2+4x. Find f′(x). f′(x)= Find the slope of the tangent line at x=4. Slope = f′(4)= Picture included for reference.
- Find dy/dx for 2 + xy = x. Please show your work to receive credit?
- If possible, find a function f such that #grad f = (4x^3+9x^2y^2, 6x^3y+6y^5)#?
- The point at which curve y=x^2-4x+3 has gradient -2?
- Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. ? xy = 24, (-6, -4)
- Find the equation of the tangent line to the curve y=x^4+2 e^x at the point (0,2)?
- Find the number a such that the line x = a divides the region bounded by the curves y = x, y = 0, and x = 4 into two regions with equal area. Give your answer correct to 3 decimal places?
- How do you find the critical points of y=x(1-x)^4? I know I need to take the derivative and I guess that's where I'm stuck. I think it's a product and a chain rule?
- How do I find a general formula for #f^(n)(x)# if #f(x)=x^-4#?
- Confused about cylindrical shell radius?
- How to solve x when give the derivative?
- ]Find the derivative of f(x) = x 2+2 cos2 (4x)?
- How to investigate the following function and plot its graph using the methods of differential calculus: y=e^[1/2(x+1)] / x+1 ?