Questions tagged 'derivative'
4 questions
the line that is normal to the curve x^2 + 2xy – 3y^2 = 0 at (1,1) intersects the curve at what other point?
I found the derivative of the curve to be: dy/dx = -(2x + 2y) / (2x - 6y). Then, I calculated the slope at the point (1, 1) and found it to be 1. This makes the slope of the normal line -1. Using this...
Jan 20, 2025
What does it mean if a function is twice differentiable?
What does it mean for a function to be twice differentiable? Does it imply that we can take its derivative two times, or does it require us to find its antiderivative twice in order to return to the o...
The derivative of f(x) = (x^4/3) – (x^5/5) attains its maximum value at x =?
Given the function ( f(x) = \frac{x^{4/3}}{1} - \frac{x^5}{5} ), at which value of ( x ) does the derivative attain its maximum value? Please show all of your work! The answer choices are: A. -1 B. 0...
What is the proof that the derivative of arccot (x) = -1/ (1+x^2)?
What is the mathematical proof that the derivative of arccot(x) is equal to -1 / (1 + x²)? Could you provide a step-by-step explanation of how this result is derived?