Gradients and Tangents

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Presentation transcript:

Gradients and Tangents Differentiation 3.6

When you find the derivative you are finding the gradient function which means you can find the gradient at any point on the curve.

(-1, 3) on line: The equation of a tangent e.g. 1 Find the equation of the tangent at the point (-1, 3) on the curve with equation Solution: The gradient of a curve at a point and the gradient of the tangent at that point are equal (-1, 3) x Gradient = -5 At x = -1 (-1, 3) on line: So, the equation of the tangent is

( We read this as “ f dashed x ” ) An Alternative Notation The notation for a function of x can be used instead of y. When is used, instead of using for the gradient function, we write ( We read this as “ f dashed x ” ) This notation is helpful if we need to substitute for x. e.g.

e.g. 2 Find the equation of the tangent where x = 2 on the curve with equation where Solution: To use we need to know y at the point as well as x and m From (1), (2, 2) on the line So, the equation of the tangent is

SUMMARY To find the equation of the tangent at a point on the curve : if the y-value at the point is not given, substitute the x -value into the equation of the curve to find y find the gradient function substitute the x-value into to find the gradient of the tangent, m substitute for y, m and x into to find c

Find the equation of the tangent to the curve 1. Exercises Find the equation of the tangent to the curve 1. at the point (2, -1) Ans: 2. Find the equation of the tangent to the curve at the point x = -1, where Ans:

Your turn page 306 Delta exercise 16.08