Max/Min Problem Quiz

Find the equation of the tangent to the curve y = x²-2 at the point where x = 3.

The curve f(x) = x³ bx² - 9x + 7 has a stationary point when x = -1. Find the value of b.

Find the stationary points of the curve y=x³-12x + 5 and determine if each point is a maximum or a minimum.

The point P(x, y) lies on the curve with equation y = 6x² - x³. (i) Find the value of x for which the gradient of the tangent at P is 12. (ii) Hence, find the equation of the tangent at P.

Find the range of values of x for which the function f(x) = x³ + 3x² - 9x is decreasing.

(i) Find the speed of the particle after 4 seconds. (ii) After how many seconds is the particle at rest?

The equation of a curve is y = x sin 2.x. Find the slope of the curve at the point where x = 3.

A particle moves in a straight line so that, after a time of t seconds, its distance s metres from a fixed point O is given by s = 21³ - 24t.

For x + y = 100, prove that product P = xy is a maximum when x = y, and find the maximum value of P.

The number of salmon swimming upstream in a river in order to spawn is approximated by s(x) = -x³ + 3x² + 360x + 5000, with x representing the temperature of the water in degrees (°C). (This function is valid only if 6≤x≤20.) Find the water temperature that results in the maximum number of salmon swimming upstream.