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# Ms2 gradient of a curve and equation

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

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### 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)