IB Mathematics Analysis and Approaches Topic SL…

Let $g(x)=\frac{\sin(2x)}{2}\left(\frac{1}{\tan(x)}+2\right)-\sin^2(x)$ .

Show that $g(x)=\sin(2x)+\cos(2x)$ .

Let $y=x^{2}\cos x$ for $x\in\mathbb{R}$ .

Let $f(x)=\frac{2 x^{3}}{x^{2}+1}$ , for . The region is bounded by the graph of , the x-axis, and the lines and .

Let $f(x) = 3x^2 - 2x + 1$ and . Both and are differentiable at .

Consider the function $y=\frac{\ln x}{x^{3}}$ , for .

Hence, using your answer from Part 2, find $\int\!g(x)\,dx$ in terms of $g'(x)$ .

Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ .

Find the equation of the tangent at $x=\frac{\pi}{2}$ .

Find $f^{\prime}(x)$ .

Show that the area of $R$ is $4-\ln 5$ .

Find the x-coordinate where the tangent to $f$ is horizontal.

Find $f^{\prime}(x)$ .

whether the gradients of the tangents to $f$ and $g$ at $x = 2$ are equal.

Find the equation of the tangent to $f$ at $x = 2$ .

Show that $\frac{d y}{d x}=\frac{1-3 \ln x}{x^{4}}$ .

Find the coordinates of the point where the tangent to the graph is horizontal.

the graph of $y=\frac{\ln x}{x^{3}}$ , indicating the x -intercept and the point from part 2.

IB Mathematics Analysis and Approaches SL 5.6—differentiating Polynomials n E Q. Chain, Product and Quotient Rules Questionbank