Question
full solution please.
Find all critical numbers of the following functions. For each critical number determine whether it represents a local maximum, a local minimum or neither (saddle point). f(x) = x3 + 3x2 Suppose that the population (in thousands) of a certain kind of insect after t months is given by the following formula P(t) = 3t+ sin(4t) + 100. Determine the minimum and maximum population in the first 3 months. A box with no top is built by taking a 6"-by-6" piece of cardboard, cutting x-in. squares out of each corner and folding up the sides. The four x-in. squares are then taped together to form a second box (with no top or bottom). Find the value of x that maximizes the sum of the volumes of the boxes. Suppose a forest fire spreads in a circle with radius changing at a rate of 5 feet per minute. When the radius reaches 200 feet, at what rate is the area of the burning region increasing?
Explanation / Answer
3)
df(x)/dx = (3x^2 + 6x)/2*(x^3+3x^2)^(1/2)
for critical pointdf(x)/dx=0
3x^2+6x=0
x(3x+6)=0
x=0; x=-2 .........................ans
