Consider the curve given by the function $f\left(x\right)=x^3+5x$f(x)=x3+5x.

Determine the gradient of the tangent at the point $\left(2,18\right)$(2,18).

At point $M$M$\left(x,y\right)$(x,y), the equation of the tangent to the curve $y=x^2$y=x2 is given by $y=4x-4$y=4x−4.

At point $M$M$\left(x,y\right)$(x,y), the equation of the tangent to the curve $y=x^3$y=x3 is given by $y=12x-16$y=12x−16.

Consider the parabola $f\left(x\right)=x^2+3x-10$f(x)=x2+3x−10.

Apply differentiation to gradients, tangents and normals.