IB Mathematics Analysis and Approaches Topic SL…

Consider the polynomial function $f(x)=x^{3}-6x^{2}+9x+k$ , where is a constant.

(a) Show that the $x$ -coordinate of P is $2$ .

(b) Find the gradient of the normal to the graph of $y=f(x)$ at P.

Let $h(x)=x^{3}-3x+2$ and $j(x)=2x-k$ , where $k$ is a constant. The line $y=j(x)$ is a normal to the graph of $y=h(x)$ at the point where $x=a$ .

(a) Find $h^{\prime}(x)$ .

(b) Show that $a=\pm\sqrt{\frac{5}{6}}$ .

The function $f$ is differentiable for all $x \in \mathbb{R}$ . The line with equation $y = 12 - 5x$ is tangent to the graph of $f$ at the point where $x = 3$ .

The curve $C$ is defined by the function $g(x)=2 x^{4}-8 x^{2}+5$ . Let $P$ be the point on $C$ where $x=1$ .

(a) Find the gradient of the tangent to $C$ at $P$ .

The curve $C$ is defined by the function $h(x)=x^{3}-6x+1$ . Let $A$ be the point on $C$ where $x=2$ .

(a) Find the gradient of the tangent to $C$ at $A$ .

(a) the value of $f(3)$ .

(b) the value of $f'(3)$ .

(d) the equation of the tangent line to the graph of $h$ at $x = 3$ .

(b) the equation of the tangent at $P$ .

(b) the equation of the tangent at $A$ .

IB Mathematics Analysis and Approaches SL 5.4—tangents and Normal Questionbank

IB Mathematics Analysis and Approaches SL 5.4—tangents and Normal Questionbank

IB Mathematics Analysis and Approaches SL 5.4—tangents and Normal Questionbank

IB Mathematics Analysis and Approaches SL 5.4—tangents and Normal Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 5.4—tangents and Normal Questionbank