Let f be the function defined by fx kx x ( ) = - ln for x > 0, where k is a positive constant.

(a) Find f ¢( ) x and f ¢¢( ) x .

(b) For what value of the constant k does f have a critical point at x = 1 ? For this value of k, determine

whether f has a relative minimum, relative maximum, or neither at x = 1. Justify your answer.

(c) For a certain value of the constant k, the graph of f has a point of inflection on the x-axis. Find this value

of k.

Ahigh-altitude spherical weather balloon expands as it rises, due to the drop in atmospheric pressure. suppose that the radius r increases at the rate of 0.02 inches per second, and that r = 36 inches at time t = 0. determine the equation that models the volume v of the balloon at time t, and find the volume when t = 360 seconds. v(t) = 4π(0.02t)2; 651.44 in3 v(t) = 4π(36 + 0.02t)2; 1,694,397.14 in3 v(t) = four pi times the product of zero point zero two and t to the third power divided by three.; 4,690.37 in3 v(t) = four pi times the quantity of thirty six plus zero point zero two t to the third power divided by three.; 337,706.83 in3

Masons cell phone company charges $0.12 for every text message he sends plus $2.50 per month if mason sent 25 messages this month how much money does he owe the one with the correct answer and explanation gets 10 points and is marked as the brainliest answer

Which answer choice is it? is it the first ,second,third or fourth giving 40 points for whoever answers correctly you