Question The curve C has equation y=f(x), x>0, where Given tht the point P(4,-8) lies on the curve C; a. find the equation of the tangent to C at P, giving your answer in the form y = mx + c, where m and c are constants. a. find f(x), giving each term in its simplest […]
Question Find giving each term in its simplest form. Solution We are given; Rule for integration of is: Rule for integration of is: Rule for integration of is:
Question Find giving each term in its simplest form. Solution We are given; Rule for integration of is: Rule for integration of is: Rule for integration of is:
Question A curve with equation y=f(x) passes through the point (4,9). Given that , x > 0 a. find f(x), giving each term in its simplest form. Point P lies on the curve. The normal to the curve at P is parallel to the line 2y + x = 0 b. Find x coordinate of […]
Question Given that , , , find in their simplest form, a. b. . Solution a. We are given; We are required to find . Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve with respect to is: Therefore; Rule for differentiation is of is: Rule for differentiation is […]
Question , Given that y=37 at x=4, find y in terms of x, giving each term in its simplest form. Solution We are given that; We are given coordinates of appoint that is y=37 at x=4 ie (4,37). We are required to find the equation of y in terms of x. We can find equation of the curve […]
Question Given that , , , find in their simplest form, a. b. . Solution a. We are given; We are required to find . Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve with respect to is: Therefore; Rule for differentiation is of is: Rule for differentiation is […]
Question A curve with equation y=f(x) passes through the point (4,25). Given that a. find f(x) simplifying each term. b. Find an equation of the normal to the curve at the point (4, 25). Give your answer in the form ax + by + c = 0, where a, b and c are integers to […]
Question Find giving each term in its simplest form. Solution We are given; Rule for integration of is: Rule for integration of is: Rule for integration of is:
Question A curve with equation y=f(x) passes through the point (3,6). Given that a. use integration to find f(x). Give your answer as a polynomial in its simplest form. b. Show that , where p is a positive constant. State the value of p. c. Sketch the graph of y = f(x), showing the coordinates of […]
Question A curve has equation y=f(x). The point P with coordinates (9,0) lies on the curve. Given that , a. Find f(x). b. Find the x-coordinates of two points on y=f(x) where the gradient of the curve is equal to 10. Solution a. We are given; We are given coordinates of a point on the […]
Question Find giving each term in its simplest form. Solution We are given; Rule for integration of is: Rule for integration of is:
Question , a. Show that Where A and B are constants to be found. b. Find Given that the point (-3,10) lies on the curve with equation y=f(x), c. Find f(x). Solution a. We are given; Therefore; b. We are given; We are required to find . Second derivative is the derivative of the derivative. […]
Question Find giving each term in its simplest form. Solution We are given; Rule for integration of is: Rule for integration of is:
Question , Given that y=7 at x=1, find y in terms of x, giving each term in its simplest form. Solution We are given that; We are given coordinates of appoint that is y=7 at x=1 ie (1,7). We are required to find the equation of y in terms of x. We can find equation of the curve […]
Question The point P(4,–1) lies on the curve C with equation y = f(x), x > 0, and a. Find the equation of the tangent to C at the point P, giving your answer in the form y = mx + c, where m and c are integers. b. Find f(x). Solution a. We are required to […]
Question Find Giving each term in its simplest form. Solution a. We are required to find; Rule for integration of is: Rule for integration of is:
Question A curve with equation y = f (x) passes through the point (2,10). Given that f ′(x) = 3×2 − 3x + 5 find the value of f (1). Solution We are required to find f(1) but we are not given f(x) but f ′(x). f ′(x) = 3×2 − 3x + 5 Therefore, we need to […]
Question Given that , , find, in their simplest form, a. b. . Solution a. We are given; We are required to find . Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve with respect to is: Therefore; Rule for differentiation is of is: Rule for differentiation is of is: […]
Question Given that can be written in the form , a. Write down the value of p and the value of q. Given that , and that y=90 when x=4; b. find in terms of x, simplifying the coefficient of each term. Solution a. We are given; b. We are required to find y […]