Karen Morrison and Nick Hamshaw Solutions for Exercise 10: Exercise 18.10

The graph of $y=x^2$ is shown in the diagram. Find the gradient of the graph at the point $\left(2,4\right)$.

The graph of $y=x^2$ is shown in the diagram. Find the gradient of the graph at the point $\left(-1,1\right)$.

The gradient of the graph at the point $(1.5,2.25)$ is $3$. Write down the coordinates of the point at which the gradient is $-3$.

The graph shows how the population of a village has changed since $1930$. Find the gradient of the graph at the point $(1950,170)$.

The graph shows how the population of a village has changed since $1930$. Find the gradient of the graph the point $(1950,170)$. What does this gradient represent.

Draw the graph of the curve $y=x^3+1$ for $x$ from $-2$ to $+2$.

Draw the graph of the curve $y=x^3+1$ for $x$ from $-2$ to $+2$. Find the gradient of the curve at the point $A(1,2)$.