List of top Applied Mathematics Questions on Differentiation

Find all the points of local maxima and local minima of the function: \[ f(x) = -\frac{3}{4}x^4 - 8x^3 - \frac{45}{2}x^2 + 105. \]
Find the differential equation of all circles in the first quadrant which touch both the coordinate axes.
The graph of the inequation \( 2x + 3y>6 \) is the:
The order and degree of the differential equation \[ y \, dx + x \, \log{\left(\frac{y}{x}\right)} \, dy - 2x \, dy = 0 \] are respectively:
If \( y = e^{-2x} \), then \( \frac{d^3y}{dx^3} \) is equal to: