Ms2 gradient of a curve and equation
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The document outlines methods for finding the gradient of a curve and the equation of tangents at specific points, emphasizing the need to differentiate and substitute values. It includes practice problems involving curves such as y=(x-3)(x+2) and y=x^2-2x+3, focusing on calculating gradients and determining tangent equations. Additional resources for mathematical studies are also referenced.
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Ms2 gradient of a curve and equation
- 1. Gradient of a Curve and Equation of a Tangent to a Curve Math Studies 2 – Topic 7
- 2. Find the gradient of the tangent to the curve whose equation is at the point where x=2.
- 3. A power boat moves in a straight line such that at time t seconds its distance s from a fixed point O on that line is given by Find the speed after 3 seconds.
- 4. Find the value of the gradient of the curve whose equation is y=(x-3)(x+2) at the point where it crosses the positive x-axis (x=3).
- 5. Think Back What are the steps I used to solve the problems?
- 6. Steps to finding the gradient of any curve Differentiate to find the gradient Substitute the particular value of x to find the gradient of the curve at that point
- 7. Find the equation of the tangent to the curve whose equation is at the point P where x=2.
- 9. Think Back What are the steps I used to solve the problems?
- 10. Equation of the Tangent at a Given Point Find the gradient at the point P and call it m Find the y-coordinate of P as well as the x-coordinate (sometimes it will be given) Use y=mx+c and substitute for m, x, and y at the point P Write the equation with values of m and c
- 12. Find the equation of the tangent to the curve whose equation is y=x²-2x +3 at the point where x=1. Show all working. Find the equation of a tangent to the curve whose equation is y=2x³-4x at the point where x=2. The curve whose equation is y=x²-4x+15 has gradient 6 when x=a. Find the value of a. The tangent to the parabola given by y=x²+3x-8 has gradient 7 at the point P. Find the coordinates of P.
- 13. Solution y=2x+4 y=20x-32 5 (2,2)
- 14. Resources www.info.oxford-consulting.com www.wclipart.com www.clipartspot.net Mathematical Studies Course Companion (Oxford)