IB Mathematics Analysis and Approaches Topic SL…

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

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

(b) Show that $g''(x)=-4g(x)$ .

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

(a) Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ .

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

Let $f(x)=\frac{2 x^{3}}{x^{2}+1}$ , for $x \in \mathbb{R}$ . The region $R$ is bounded by the graph of $f$ , the x-axis, and the lines $x=0$ and $x=2$ .

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

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

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

Consider the function $y=\frac{\ln x}{x^{3}}$ , for $x>0$ .

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

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

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

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

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

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

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

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

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