6 A curve has equation y=x^5-2x^2+9 . The point P with coordinates (-1, 6) lies on the curve.(a) Find the equation of the tangent to the curve at the point P. giving your answer in the form y = mx+ c.(b) The point Q with coordinates (2, k) lies on the curve.(i)...
11. The curve C has equation y=2x-8√(x+5) ,x≥0(a) sind(dy)/(dx) , giving each term in its simplest form.(3)The point P on C has x-coordinate equal to(b)Find the equation of the tangent to C at the point P, giving your answer in the form y= ax + b, whe...
[5] 11 A curve has equation y = kx − 3−1 + kx − 3, where k is a non-zero constant. (i) Find the x-coordinates of the stationary points in terms of k, and determine the nature of each stationary point, justifying your answers. [7] (ii) y 2 x O y = x − 3...
[2] (c) Find the area of the shaded region bounded by the curve and the coordinate axes. [2] © UCLES 2020 9709/12/O/N/20 [Turnover PMT 16 11 A curve has equation y = 3 cos 2x + 2 for 0 ≤ x ≤π. (a) State the greatest and least values of y. [2] (b) Sketch ...
Suppose a curve is defined by the equation {eq}\displaystyle \frac {y} {y - x} = x^2 -1 {/eq}. Find {eq}\displaystyle \frac {dx}{dy} {/eq}. Implicit Differentiation: At first, simplify the give implicit equation to eliminate the fraction on the left hand sid...
Consider the curve defined by the equation xy=7. Set up an integral to find the length of curve from x=a to x=b. Arc Length The length L of any given curve f(x) over the interval [a,b] can be found by using the formula L=∫ab1...
x and the point P (2, 9) lies on the curve. The normal to the curve at P dx meets the curve again at Q. Find (i) the equation of the curve, [3] (ii) the equation of the normal to the curve at P, [3] (iii) the coordinates of Q. [3] 1 A curve has equation y = ...
9.O28X AFigure 3Figure 3 shows a sketch of the curve with equation y = f(x)where f(x)=8/x+1/2x-5 , 0x≤12 The curve crosses the x-axis at (2, 0) and (8, 0) and has a minimum point at A.(a)Use calculus to find the coordinates of point A.(5)(b)State(i) the ...
Write a parametric equation and a vector equation of the curve intersecting x2+y2=1andy+z=2 Parametric equation A parametric equation is an equation in which we express the set of quantity as an explicit function of independent variables which is known as...
Use the equation given to calculate the slope of a line tangent to y=4x2+3x at P(−3,27). mPQ=f(x1+h)−f(x1)hSlopes and Tangents:To find the slope o the curve, we can use two methods, one is the definition of the derivative meth...