Question A curve has equation . a. Find b. Find an equation for the tangent to the curve at the point where . c. Determine whether is increasing or decreasing when . Solution a. We have the equation; Rule for differentiation is of is: Rule for differentiation is of is: Rule for differentiation is of is: b. […]
Question The point has coordinates and the point has coordinates . a. i. Find the gradient of the line . ii. Hence, or otherwise, show that the line has equation b. The line intersects the line with equation at the point . Find the coordinates of . c. Find an equation of the line through which is perpendicular to . Solution a. […]
Question The diagram shows the curve with equation and the line . The points and have coordinates and respectively. The curve touches the x-axis at the origin and crosses the x-axis at the point . The line cuts the curve at the point where and touches the curve at where . a. Find the area of the rectangle . b. i. […]
Question a. i. Express in the form , where and are integers. ii. Hence, or otherwise, describe the coordinates of the minimum point of the curve with equation . b. The line has equation and the curve has the equation . i. Show that the x-coordinates of the points of […]
Question The point has coordinates and the point has coordinates . The line has equation . a. i. Show that . ii. Hence find the coordinates of the mid-point of . b. Find the gradient of . c. Line is perpendicular to the line . i. Find the gradient of . ii. Hence find the equation of the line . iii. Given that point […]