Презентация, доклад по математике Производная функции, свойства производной, 10 класс

We need to be able to find these points using algebra Gradient of curve= gradient of tangent= 4Points with a Given Gradient

Слайд 1Made by ALEX
P1 Chapter 7.1
«Tangents and Gradients»

Made by ALEXP1 Chapter 7.1«Tangents and Gradients»

Слайд 2We need to be able to find these points using algebra

Gradient of curve
= gradient of tangent
= 4

Points with a Given Gradient

We need to be able to find these points using algebra Gradient of curve= gradient of tangent=

Слайд 3Points with a Given Gradient
Gradient is 4

Points with a Given GradientGradient is 4

Слайд 4Points with a Given Gradient

Points with a Given Gradient

Слайд 5SUMMARY
To find the point(s) on a curve

with a given gradient:

solve the resulting equation

SUMMARYTo find the point(s) on a curve       with a given gradient:solve

Слайд 6Find the coordinates of the points on the curves with the

gradients given

where the gradient is -2

1.

where the gradient is 3

2.

Ans: (-3, -6)

Ans: (-2, 2) and (4, -88)

( Watch out for the common factor in the quadratic equation )

Exercises

Find the coordinates of the points on the curves with the gradients given where the gradient is

Слайд 7Increasing and Decreasing Functions

Increasing and Decreasing Functions

Слайд 8a positive number ( 3 ) × a perfect square (

which is positive or zero for all values of x, and

a positive number ( 4 )

a positive number ( 3 ) × a perfect square ( which is positive or zero for

Слайд 11Exercises
Solutions are on the next 2 slides.

ExercisesSolutions are on the next 2 slides.

Слайд 121. Show that is a decreasing

function and sketch its graph.

Solutions

1. Show that      is a decreasing function and sketch its graph.Solutions

Слайд 13Solutions
and a positive number. Hence y is an increasing function.

Solutionsand a positive number. Hence y is an increasing function.

Слайд 14The equation of a tangent

The equation of a tangent

Слайд 15An Alternative Notation
( We read this as “ f dashed

x ” )

This notation is helpful if we need to substitute for x.

An Alternative Notation ( We read this as “ f dashed x ” )This notation is helpful

Слайд 16From (1),

(2, 2) on the line

From (1),(2, 2) on the line

Слайд 17if the y-value at the point is not given, substitute the

x -value into the equation of the curve to find y

SUMMARY

if the y-value at the point is not given, substitute the x -value into the equation of

Слайд 18Exercises
Ans:
Ans:
Find the equation of the tangent to the curve
2.
at the point

x = -1, where
ExercisesAns:Ans:Find the equation of the tangent to the curve2.at the point x = -1, where

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