Karen Morrison and Nick Hamshaw Solutions for Exercise 13: Exercise 18.13

Differentiate
$y=\left(x+3\right)\left(x-3\right)$

Find the gradient of the curve with equation $y=\left(3x-2\right)\left(4x+1\right)$ at the points with the coordinates $\left(3,91\right)$.

Find the point at which gradient of the curve with equation $y=3x^2-4x+1$ is zero.

Find the coordinates of the point on the curve with equation $y=3x^2-4x-2$,where the curve is parallel to the line with equation $y=-2x+1$

Find the coordinates of the point on the curve with equation $y=2x^3-9x^2+12x$,where the curve with is parallel to the $x$-axis.

 The curve with equation $y=x^3+3$ has two tangents,parallel to the line with equation $y=12x-1$.Find the coordinates of the two points.

 The curve with equation $y=a{x}^3-4x+1$,parallel to the line with equation $y=50x-1$ at the point with $x$-coordinate $3$.Find the gradient of the curve with $x$-coordinates $4$

 The curve with equation $y=a{x}^3-4x+1$,parallel to the line with equation $y=50x-1$ at the point with $x$-coordinate $3$.Show the tangent at the point with $x$-coordinates $-3$ is also parallel to the same line.