Karen Morrison and Nick Hamshaw Solutions for Exercise 15: Exercise 18.15

Find the turning point or points on the given curve explain the point is maximum or minimum
$y=x\left(2x-3\right)$

Find the turning point or points on the given curve explain the point is maximum or minimum
$y=x\left(2x^2-21x+72\right)$

Find the turning point or points on the given curve explain the point is maximum or minimum
$y=x^2\left(3-x\right)$

The height $h metres$ of a ball above the ground is given by the formula $h=7t-5t^2$ at time $t sec.$ after the ball is thrown upwards.Find $\frac{dh}{dt}$

The height $h metres$ of a ball above the ground is given by the formula $h=7t-5t^2$ at time $t sec.$ after the ball is thrown upwards.Find the greatest height of the ball above the ground.

The cube of a number is $152$ more than the cube of another number that is $2$ smaller. What are the two possible numbers for which this is true.

The given diagram shows,an open topped cylinder with radius $r cm$ and height $12 cm$.If the outer surface area is $81\pi c{m}^2$,find the radius of the cylinder.

The product of two consecutive integers is $11$ more than $3$ times their sum. What are the pairs of integers which meet these conditions