Finding the Gradient of a Curve

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

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 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.

Work out the equation of the line in the form: $y=mx+c$

For the given straight line from$\left(-1,1\right)$ to $\left(3,5\right)$  on the grid work out to find the gradient of this line.

On the grid, draw a straight line from $\left(-1,1\right)$ to $\left(3,5\right)$

Write down the equation of this line of symmetry for $y=5+3x-x^2$.

On the grid, draw the line of symmetry of $y=5+3x-x^2$

Use the graph of $y=5+3x-x^2$ to solve the equation $5+3x-x^2=0$

On the grid, draw the graph of $y=5+3x-x^2$ for $-2⩽x⩽5$ with the help of the table:

Complete the table for $y=5+3x-x^2$

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 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 $\frac{dh}{dt}$

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

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
$y=x\left(2x-3\right)$

Find the turning point or points on the given curve explain the point is maximum or minimum
$y=-x^3+6x^2+3$

Find the turning point or points on the given curve explain the point is maximum or minimum
$y=\left(x-5\right)\left(x+5\right)$

Find the turning point or points on the given curve explain the point is maximum or minimum
$y=x\left(x-4\right)$

Find the turning point or points on the given curve explain the point is maximum or minimum
$y=x^3-12x+1$