Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Ms2 gradient of a curve and equation

3,492 views

Published on

Math Studies Year 2 - Intro to Calculus
Find gradient of a curve and equation of a tangent to a curve

Published in: Education, Technology
  • Be the first to comment

  • Be the first to like this

Ms2 gradient of a curve and equation

  1. 1. Gradient of a Curve and Equation of a Tangent to a Curve Math Studies 2 – Topic 7
  2. 2. Find the gradient of the tangent to the curve whose equation is at the point where x=2.
  3. 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. 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. 5. Think Back What are the steps I used to solve the problems?
  6. 6. Steps to finding the gradient of any curve <ul><li>Differentiate to find the gradient </li></ul><ul><li>Substitute the particular value of x </li></ul><ul><li>to find the gradient of the curve at that point </li></ul>
  7. 7. Find the equation of the tangent to the curve whose equation is at the point P where x=2.
  8. 9. Think Back What are the steps I used to solve the problems?
  9. 10. Equation of the Tangent at a Given Point <ul><li>Find the gradient at the point P and call it m </li></ul><ul><li>Find the y-coordinate of P as well as the x-coordinate (sometimes it will be given) </li></ul><ul><li>Use y=mx+c and substitute for m, x, and y at the point P </li></ul><ul><li>Write the equation with values of m and c </li></ul>
  10. 11. Independent Practice
  11. 12. <ul><li>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. </li></ul><ul><li>Find the equation of a tangent to the curve whose equation is y=2x³-4x at the point where x=2. </li></ul><ul><li>The curve whose equation is y=x²-4x+15 has gradient 6 when x=a. Find the value of a. </li></ul><ul><li>The tangent to the parabola given by y=x²+3x-8 has gradient 7 at the point P. Find the coordinates of P. </li></ul>
  12. 13. <ul><li>Solution </li></ul><ul><li>y=2x+4 </li></ul><ul><li>y=20x-32 </li></ul><ul><li>5 </li></ul><ul><li>(2,2) </li></ul>
  13. 14. Resources www.info.oxford-consulting.com www.wclipart.com www.clipartspot.net Mathematical Studies Course Companion (Oxford)

×