Practice section 2 of 8

The diagram shows a sketch of $y=f(x)$. (a) State the range of x for which f is strictly decreasing. (b) Sketch $y=f^{\prime}(x)$ on a separate diagram for all x.

The diagram shows the graph of $y=f(x)$. Sketch the curve of $y=f^{\prime}(x)$.

Example 8 (Self-Reading): $P$ is the point $(4,7)$ on the curve $y=x^2-6x+15$. Find the gradient of the curve at $P$ and the equation of the tangent at this point.

Find the equation of the tangent to the curve $y=3x^2-4x+5$ at the point $(1,4)$.

A curve is defined by the equation $x^3+y^3+3xy-1=0$. Find the equation of the normal to the curve at the point $(2,-1)$.

A curve is defined by $\sin x+\cos y=1$, $0\le x,y\le\pi/2$. Find the exact equation of the normal at $(\pi/6,\pi/3)$.