Math 16a worksheet 10 a tank has the shape of an upside

Question

MATH 16A WORKSHEET 10-

(1) Suppose x and y are both differentiable functions of t and are related by the equation y⁴ - x² = 1. Use implicit differentiation with respect to t to determine dy/dt in terms of x, y, dx/dt .

(2) A tank has the shape of an upside down cone with radius 3 meters and height 4 meters. Water is pouring into the tank at 2 cubic meters per second. How fast is the water level rising when the water level is 3 meters high?

(3) Solve the equation 2^2x - 2^x+2 - 32 = 0 for x.

(4) Find f' and f'' for f(x) = e^x2-x. Find the absolute minimum and explain why it is an absolute minimum.

(5) Find the derivative of the following functions.

(a) f(x) = ln √x

(b) f(t) = (ln(e^2t + 1))²

(c) f(x) = ln(x ln(x + 1)).