Question

# Short answer problems. A correct answer in the box gives full marks. For partial marks work needs to be shown. Derivatives Derivatives The values of f(r) are as given in the table. a. Based on the above table, provide the best estimate for f'(x) and fill in the second table. \text { b. Estimate } f^{\prime \prime}(2.0) \text {. } f^{\prime \prime}(2.0)= \text { Find the derivative of } f(x)=\frac{x}{\ln \left(\frac{1}{x}\right)} \frac{d f}{d x}= \text { i. (2 points) Consider the curve } e^{2 x}+y(1-x)=1 \text {. Find } \frac{u y}{d x} \text { at the point } x=0 \text {. } Find the equation of the tangent line y = mx + b to the graph of f(x)=\cos (\pi x) \text { at } x=1 / 2 \text { Let } f^{-1} \text { be the inverse function of } f(x) \text {. Assume } f(0)=1 \text { and } f^{\prime}(0)=2 \text {. } Find the tangent line y = mx + b to ƒ-'1(x) at 1.  Fig: 1  Fig: 2  Fig: 3  Fig: 4  Fig: 5  Fig: 6  Fig: 7  Fig: 8  Fig: 9  Fig: 10  Fig: 11  Fig: 12  Fig: 13  Fig: 14  Fig: 15  Fig: 16